(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 71313, 1932] NotebookOptionsPosition[ 64878, 1819] NotebookOutlinePosition[ 65286, 1836] CellTagsIndexPosition[ 65243, 1833] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "\n", StyleBox["Blockchain Model--SA pay for BEL\n", "Subtitle"], StyleBox["The VM\[CloseCurlyQuote]s Effort Under Insurance Model", "Section"], "\n" }], "Text", CellChangeTimes->{{3.8594477754364*^9, 3.8594478013069963`*^9}, 3.859447848801239*^9},ExpressionUUID->"8da70118-74ed-4ef1-86e6-\ 26d1ad97f2f4"], Cell[BoxData[{ RowBox[{"Profitvb", ":=", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", RowBox[{"eb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], "\[Theta]"}], "-", RowBox[{"kb", "*", RowBox[{"(", RowBox[{"eb", "*", "eb"}], ")"}]}], "-", "cv"}]}], "\[IndentingNewLine]", RowBox[{"Profitib", ":=", RowBox[{ RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}]}]}], "\[IndentingNewLine]", RowBox[{"Profitsb", ":=", RowBox[{ RowBox[{ RowBox[{"-", "\[Alpha]"}], " ", "pb"}], "+", RowBox[{"eb", RowBox[{"(", RowBox[{"f", "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}]}], ")"}]}], "-", "cs", " ", "-", RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", "csb", " ", "-", "cvb"}]}]}], "Input", CellChangeTimes->{{3.84774692485349*^9, 3.847746972128188*^9}, { 3.847747397472211*^9, 3.8477474241671333`*^9}, {3.847747702882146*^9, 3.847747709330879*^9}, {3.847747747143688*^9, 3.8477477763814287`*^9}, { 3.847749431163137*^9, 3.8477494324598417`*^9}, {3.84793877916921*^9, 3.847938800764226*^9}, {3.859447859574151*^9, 3.859447873769586*^9}, { 3.8594484971353807`*^9, 3.859448502862301*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"06fa2129-7c21-4d8b-a4e6-74232a429dd9"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"D", "[", RowBox[{"Profitvb", ",", "eb"}], "]"}]], "Input", CellChangeTimes->{{3.847747574908453*^9, 3.847747592385933*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"9907c7dd-e61f-4f2c-b9f6-bedf58db12e4"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "eb", " ", "kb"}], "+", RowBox[{"pb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}]], "Output", CellChangeTimes->{3.859447906053748*^9}, CellLabel->"Out[4]=",ExpressionUUID->"ed2c5394-980c-43ea-a6d5-499bc8710fec"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"%", "\[Equal]", "0"}], ",", "eb"}], "]"}]], "Input", CellChangeTimes->{{3.8477475972713127`*^9, 3.847747624762442*^9}}, CellLabel->"In[5]:=",ExpressionUUID->"e4d26ebd-3078-4e62-8ebd-aa5b21fb3b60"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"eb", "\[Rule]", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.859447935758842*^9}, CellLabel->"Out[5]=",ExpressionUUID->"045c1f00-27a8-472e-8e3f-59be3f6a17a7"] }, Open ]], Cell[TextData[{ "We now solve the Stackelberg game by using backward induction. First, \ given any contingent price ", Cell[BoxData[ FormBox[ SuperscriptBox["p", "B"], TraditionalForm]],ExpressionUUID-> "fa06be36-ffe6-4f22-9734-125fa55a66e7"], " , by considering the first-order condition of Profitv, the vehicle \ manufacture\[CloseCurlyQuote]s best response is given as\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"e", "^", "B"}], "=", FractionBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}], "+", "\[Theta]"}], RowBox[{"2", SuperscriptBox["k", "B"]}]]}], TraditionalForm]],ExpressionUUID-> "582c7312-2f36-4307-8a8d-2d4fdcf8e72f"], "\n" }], "Text", CellChangeTimes->{{3.8594479671801863`*^9, 3.8594479950407753`*^9}},ExpressionUUID->"5dfded16-bb8c-4e5b-9705-\ 0033db33afac"], Cell[BoxData[ RowBox[{"eb", ":=", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}]], "Input", CellChangeTimes->{{3.8477479605433083`*^9, 3.847747969736373*^9}}, CellLabel->"In[5]:=",ExpressionUUID->"1edb5d18-7f61-46ca-b234-9aed4bf11240"], Cell[CellGroupData[{ Cell[BoxData["Profitvb"], "Input", CellChangeTimes->{{3.859448001783947*^9, 3.859448005727776*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"00f0560b-8850-4cfa-b12d-39a8e260b8c1"], Cell[BoxData[ RowBox[{ RowBox[{"-", "cv"}], "+", RowBox[{"pb", " ", "\[Alpha]"}], "+", FractionBox[ RowBox[{"pb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "-", FractionBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}], "2"], RowBox[{"4", " ", "kb"}]], "-", RowBox[{"\[Theta]", " ", RowBox[{"(", RowBox[{"1", "-", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], ")"}]}]}]], "Output", CellChangeTimes->{3.8594480069936*^9}, CellLabel->"Out[7]=",ExpressionUUID->"70037904-6240-4d0e-bb96-c5db95b09629"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"-", "cv"}], "+", RowBox[{"pb", " ", "\[Alpha]"}], "+", FractionBox[ RowBox[{"pb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "-", FractionBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}], "2"], RowBox[{"4", " ", "kb"}]], "-", RowBox[{"\[Theta]", " ", RowBox[{"(", RowBox[{"1", "-", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], ")"}]}]}], "]"}]], "Input", NumberMarks->False, CellLabel->"In[8]:=",ExpressionUUID->"356391f7-c78a-491a-af2d-bb84c0b1fbbf"], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "cv", " ", "kb"}], "+", RowBox[{ SuperscriptBox["pb", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"\[Theta]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", "kb"}], "+", "\[Theta]"}], ")"}]}], "+", RowBox[{"2", " ", "pb", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]}], RowBox[{"4", " ", "kb"}]]], "Output", CellChangeTimes->{3.8594480097704353`*^9}, CellLabel->"Out[8]=",ExpressionUUID->"cf0f6104-b064-4192-ac24-a46cb7502d8c"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"%", "\[Equal]", "0"}], ",", "pb"}], "]"}]], "Input", CellChangeTimes->{{3.847747934928581*^9, 3.847747945655068*^9}, { 3.847747990074339*^9, 3.847747990316766*^9}, {3.847749510013332*^9, 3.847749510233822*^9}}, CellLabel->"In[9]:=",ExpressionUUID->"7760dcc2-2bc2-448e-8c89-2717c75dc48e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pb", "\[Rule]", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}], "}"}], ",", RowBox[{"{", RowBox[{"pb", "\[Rule]", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.859448041473843*^9}, CellLabel->"Out[9]=",ExpressionUUID->"c00eb01c-76d5-4fc2-a07f-e522e1767a89"] }, Open ]], Cell[TextData[{ "Hence the vehicle manufacture\[CloseCurlyQuote]s participation condition, \ i.e., Profitv\[GreaterEqual]0, can be written as \n", Cell[BoxData[ RowBox[{"pb", ">", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}]], CellChangeTimes->{3.859448041473843*^9},ExpressionUUID-> "9e8f548c-95b2-4269-8e11-14bd779c39ef"] }], "Text", CellChangeTimes->{{3.85944806502345*^9, 3.859448117148883*^9}},ExpressionUUID->"baf5aa37-09b4-413c-9689-\ 23e912903e55"], Cell[TextData[{ StyleBox["The IC\[CloseCurlyQuote]s Premium Rate Under Blockchain Model", "Section"], "\nObserving the contract price p selected by the satellite owner, the \ insurance company can anticipate the vehicle manufacture\[CloseCurlyQuote]s \ effort e as given above. Operating in a competitive insurance market, the \ insurance company sets its premium rate r to breakeven in expectation. In \ other words, under the premium rate r that it offers, the insurance company\ \[CloseCurlyQuote]s expected profit,", StyleBox["r(\[Alpha] p+cs+f)", FontColor->RGBColor[1, 0, 0]], ", equals the expected coverage \n", StyleBox["(1-e) (\[Alpha] p+cs+f).", FontColor->RGBColor[1, 0, 0]], "\nSubstituting e given in", Cell[BoxData[ StyleBox[ RowBox[{"e", ":=", FractionBox[ RowBox[{ RowBox[{"p", RowBox[{"(", RowBox[{"1", "-", " ", "\[Alpha]"}], ")"}]}], "+", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox["k", "B"]}]]}], FontColor->RGBColor[1, 0, 0]]], CellChangeTimes->{{3.847072090450409*^9, 3.847072097890996*^9}, { 3.847074047134727*^9, 3.847074085951888*^9}},ExpressionUUID-> "f5ca7b44-ca82-466b-ab37-ea00004ae183"], " , the insurance company breakeven condition can be satisfied if and only \ if", StyleBox[" p \[GreaterEqual] ", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FormBox[ SuperscriptBox["p", "IA"], TraditionalForm]], FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "6c2046d6-632e-4840-ae4f-96256e7b407a"], StyleBox[" \[Congruent]", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"2", " ", RowBox[{"k", "^", "B"}], " ", RowBox[{"(", RowBox[{"1", "-", "r"}], ")"}]}], "-", " ", "\[Theta]"}], RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " "}]]], CellChangeTimes->{3.8470757908903217`*^9}, FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "50789a63-a33a-47ae-96bc-b4337dc208bf"], " ,which we refer as the ", StyleBox["insurance company\[CloseCurlyQuote]s underwriting constraint", FontColor->RGBColor[1, 0, 0]], ". And the premium rate satisfied with ", Cell[BoxData[ RowBox[{"r", "=", FractionBox[ RowBox[{ RowBox[{"2", " ", SuperscriptBox["k", "B"]}], "-", RowBox[{"p", RowBox[{"(", RowBox[{"1", "-", " ", "\[Alpha]"}], ")"}]}], "-", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox["k", "B"]}]]}]], CellChangeTimes->{3.847327419294375*^9}, FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "4ab4fc3e-5bce-4652-b450-4fbb35ac626c"] }], "Text", CellChangeTimes->{{3.8477529191029577`*^9, 3.8477529268173313`*^9}, { 3.8477530346284513`*^9, 3.847753035168612*^9}, {3.847753368807086*^9, 3.847753376803918*^9}, {3.84775342883288*^9, 3.8477534814311123`*^9}, { 3.847753520141313*^9, 3.847753522236432*^9}, {3.8478701916038446`*^9, 3.847870195642421*^9}},ExpressionUUID->"cd4aa122-c8d1-455a-b063-\ 43463770f7a2"], Cell[BoxData[ RowBox[{"Profitib", ":=", RowBox[{ RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}]}]}]], "Input", CellChangeTimes->{3.859448528328466*^9}, CellLabel->"In[4]:=",ExpressionUUID->"d9b09ccc-4498-44c3-81ff-ab17d5a7d3d3"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"Profitib", "\[Equal]", "0"}], ",", "rb"}], "]"}]], "Input", CellChangeTimes->{{3.847752971073448*^9, 3.8477529789299994`*^9}, { 3.847753019292562*^9, 3.847753026650053*^9}, 3.8594485307424803`*^9}, CellLabel->"In[6]:=",ExpressionUUID->"4eb450a1-f7d3-47d5-acdd-f6aa6748565f"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"rb", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"2", " ", "kb"}], "-", "pb", "+", RowBox[{"pb", " ", "\[Alpha]"}], "-", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.859448583656502*^9}, CellLabel->"Out[6]=",ExpressionUUID->"5c7992db-59bf-4242-8e46-1c2d13ec2f77"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.859448546392169*^9, 3.859448546393196*^9}},ExpressionUUID->"d5bb36e8-fbe8-4b04-aa43-\ d72d323f6367"], Cell[CellGroupData[{ Cell[TextData[StyleBox["The SO\[CloseCurlyQuote]s Optimal Contract when she \ pay for the BEL", "Section"]], "Subsubsection", CellChangeTimes->{{3.8470768941909723`*^9, 3.847076937239661*^9}, { 3.847753509270722*^9, 3.8477535139856033`*^9}, {3.859448212077497*^9, 3.859448226482435*^9}},ExpressionUUID->"100ae43e-10c0-4da8-b44d-\ 0c7d244eac83"], Cell[BoxData[{ RowBox[{"eb", ":=", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], "\[IndentingNewLine]", RowBox[{"rb", ":=", FractionBox[ RowBox[{ RowBox[{"2", " ", "kb"}], "-", "pb", "+", RowBox[{"pb", " ", "\[Alpha]"}], "-", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], "\[IndentingNewLine]", RowBox[{"Profitsb", ":=", RowBox[{ RowBox[{ RowBox[{"-", "\[Alpha]"}], " ", "pb"}], "+", RowBox[{"eb", RowBox[{"(", RowBox[{"f", "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}]}], ")"}]}], "-", "cs", " ", "-", RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", "csb", "-", "cvb"}]}]}], "Input", CellChangeTimes->{{3.847753541945079*^9, 3.847753558336581*^9}, 3.847964091568811*^9, {3.859448234924757*^9, 3.8594482392899847`*^9}, 3.859448483882091*^9}, CellLabel->"In[7]:=",ExpressionUUID->"63b57c6a-6890-4163-a939-1e97c2548b22"], Cell[CellGroupData[{ Cell[BoxData["Profitsb"], "Input", CellChangeTimes->{{3.859448245046524*^9, 3.859448248183028*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"dc9d14a8-dc93-44e7-9988-f16aa4bbf5a8"], Cell[BoxData[ RowBox[{ RowBox[{"-", "cs"}], "-", "csb", "-", "cvb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"cs", "+", "f", "+", RowBox[{"pb", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "kb"}], "-", "pb", "+", RowBox[{"pb", " ", "\[Alpha]"}], "-", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"f", "-", RowBox[{"pb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "+", RowBox[{ RowBox[{"(", RowBox[{"cs", "+", "f", "+", RowBox[{"pb", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "-", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], ")"}]}]}]], "Output", CellChangeTimes->{3.859448249011818*^9, 3.859448334161148*^9, 3.8594486024499903`*^9}, CellLabel->"Out[10]=",ExpressionUUID->"a2d6fa11-cd66-4278-8ced-963a216a81a1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"-", "cs"}], "-", "csb", "-", "cvb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"cs", "+", "f", "+", RowBox[{"pb", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", "kb"}], "-", "pb", "+", RowBox[{"pb", " ", "\[Alpha]"}], "-", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"f", "-", RowBox[{"pb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], RowBox[{"2", " ", "kb"}]], "+", RowBox[{ RowBox[{"(", RowBox[{"cs", "+", "f", "+", RowBox[{"pb", " ", "\[Alpha]"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "-", FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]]}], ")"}]}]}], "]"}]], "Input", NumberMarks->False, CellLabel->"In[11]:=",ExpressionUUID->"9db77f90-bbef-4891-9547-982e77e080ac"], Cell[BoxData[ RowBox[{"-", RowBox[{ FractionBox["1", RowBox[{"2", " ", "kb"}]], RowBox[{"(", RowBox[{ RowBox[{"2", " ", "cs", " ", "kb"}], "+", RowBox[{"2", " ", "csb", " ", "kb"}], "+", RowBox[{"2", " ", "cvb", " ", "kb"}], "-", RowBox[{"f", " ", "pb"}], "+", SuperscriptBox["pb", "2"], "+", RowBox[{"f", " ", "pb", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", "kb", " ", "pb", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", SuperscriptBox["pb", "2"], " ", "\[Alpha]"}], "+", RowBox[{ SuperscriptBox["pb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "-", RowBox[{"f", " ", "\[Theta]"}], "+", RowBox[{"pb", " ", "\[Theta]"}], "-", RowBox[{"pb", " ", "\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]}]], "Output",\ CellChangeTimes->{3.859448607650576*^9}, CellLabel->"Out[11]=",ExpressionUUID->"3d9f6c75-9526-43a8-8de5-716065173c63"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"D", "[", RowBox[{"%", ",", "pb"}], "]"}]}]], "Input", CellChangeTimes->{{3.859448351582663*^9, 3.8594483602746077`*^9}, 3.8594486180643044`*^9}, CellLabel->"In[12]:=",ExpressionUUID->"e5e300b9-8010-4af3-b52a-3fa809d8e524"], Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"-", "f"}], "+", RowBox[{"2", " ", "pb"}], "+", RowBox[{"f", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", RowBox[{"4", " ", "pb", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", "pb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", "kb"}]]}]], "Output", CellChangeTimes->{3.859448361624105*^9, 3.859448620940027*^9}, CellLabel->"Out[12]=",ExpressionUUID->"fb6222d9-df24-4b40-aab1-eb87eb098b90"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"%", "\[Equal]", "0"}], ",", "pb"}], "]"}]], "Input", CellChangeTimes->{{3.85944840169116*^9, 3.859448416413166*^9}}, CellLabel->"In[13]:=",ExpressionUUID->"121c8452-1aca-47e5-a47a-1b31b7eecdb9"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"pb", "\[Rule]", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.859448417529365*^9, 3.859448627583733*^9}, CellLabel->"Out[13]=",ExpressionUUID->"e1f49118-7f19-48dc-853a-f955feeda155"] }, Open ]], Cell[TextData[{ "for the satellite owner, her unconstrained optimal contract (p,\[Alpha]) \ can be written as ", Cell[BoxData[ StyleBox[ RowBox[{"p", "=", FractionBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"f", "-", "\[Theta]"}], ")"}], RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["k", "B"], " ", "\[Alpha]", " "}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]}]]}], FontColor->RGBColor[1, 0, 0]]], CellChangeTimes->{3.847335457059067*^9},ExpressionUUID-> "75bc1e32-c548-465f-8545-7dffb23bdb1d"], "\ns.t. p \[GreaterEqual] ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{ SuperscriptBox["k", "B"], RowBox[{"(", RowBox[{"cv", " ", "+", "cvb"}], ")"}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{ SuperscriptBox["\[Alpha]", "2"], SuperscriptBox[ SuperscriptBox["k", "B"], "2"]}], " ", "+", RowBox[{ SuperscriptBox["\[Theta]k", "B"], " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], " ", ")"}]}]}]]}], " ", "-", RowBox[{"2", " ", SuperscriptBox["k", "B"], " ", "\[Alpha]"}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", "\[Theta]"}]}], RowBox[{" ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]}]], TraditionalForm]], "Subsection",ExpressionUUID->"af705767-62a5-4775-a26f-d9a82be4ec09"], " ( the level of price that vehicle manufacture will accept)" }], "Text", CellChangeTimes->{ 3.8594484438447857`*^9},ExpressionUUID->"18005770-317f-4c40-a3a2-\ 9474f3709773"], Cell[BoxData[ RowBox[{"\[CapitalDelta]p", ":=", RowBox[{ StyleBox[ FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], FontColor->RGBColor[1, 0, 0]], StyleBox["-", FontColor->RGBColor[1, 0, 0]], FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}]}]], "Input", CellChangeTimes->{{3.859448762531652*^9, 3.859448764152492*^9}}, CellLabel->"In[14]:=",ExpressionUUID->"69075f88-39c0-49f6-91ca-c8d173fe15d9"], Cell[CellGroupData[{ Cell[BoxData["\[CapitalDelta]p"], "Input", CellLabel->"In[15]:=",ExpressionUUID->"f8bad67e-6668-4273-a625-d80e056d081d"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}]], "Output", CellChangeTimes->{3.85944878457603*^9}, CellLabel->"Out[15]=",ExpressionUUID->"36b30de3-7e6f-492d-abd7-3a8a3db339f1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", RowBox[{"2", " ", SqrtBox[ RowBox[{ RowBox[{"cv", " ", "kb"}], "-", RowBox[{"2", " ", "cv", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{"cv", " ", "kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{ SuperscriptBox["kb", "2"], " ", SuperscriptBox["\[Alpha]", "2"]}], "+", RowBox[{"kb", " ", "\[Theta]"}], "-", RowBox[{"kb", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], RowBox[{"1", "-", RowBox[{"2", " ", "\[Alpha]"}], "+", SuperscriptBox["\[Alpha]", "2"]}]]}], "]"}]], "Input", NumberMarks->False, CellLabel->"In[16]:=",ExpressionUUID->"ac941077-927d-4535-91d8-07c3cbfb6f59"], Cell[BoxData[ FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", RowBox[{"4", " ", SqrtBox[ RowBox[{"kb", " ", RowBox[{"(", RowBox[{ RowBox[{"cv", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]], "Output", CellChangeTimes->{3.859448793539484*^9}, CellLabel->"Out[16]=",ExpressionUUID->"03126934-5ebe-4a85-80dc-0bae79be173e"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"%", "\[Equal]", "0"}], ",", "f"}], "]"}]], "Input", CellChangeTimes->{{3.859448811909979*^9, 3.8594488197718782`*^9}}, CellLabel->"In[17]:=",ExpressionUUID->"334e5b24-49b5-4394-b491-699e9c900b5c"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"f", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"kb", " ", "\[Alpha]"}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], "-", FractionBox["\[Theta]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"\[Alpha]", " ", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"2", " ", SqrtBox[ RowBox[{"kb", " ", RowBox[{"(", RowBox[{ RowBox[{"cv", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], RowBox[{ FractionBox["1", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox["\[Alpha]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.859448820910637*^9}, CellLabel->"Out[17]=",ExpressionUUID->"6e22bbf4-7bcf-45e6-a3e6-d94d2f731d46"] }, Open ]], Cell[BoxData[{ RowBox[{"kb", ":=", "60"}], "\[IndentingNewLine]", RowBox[{"k", ":=", "100"}], "\[IndentingNewLine]", RowBox[{"cv", ":=", "30"}], "\[IndentingNewLine]", RowBox[{"cvb", ":=", "10"}], "\[IndentingNewLine]", RowBox[{"\[Theta]", ":=", "80"}], "\[IndentingNewLine]", RowBox[{"f1", ":=", FractionBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"kb", " ", "\[Alpha]"}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], "-", FractionBox["\[Theta]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"\[Alpha]", " ", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"2", " ", SqrtBox[ RowBox[{"kb", " ", RowBox[{"(", RowBox[{ RowBox[{"cv", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"cvb", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], RowBox[{ FractionBox["1", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox["\[Alpha]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]]}], "\[IndentingNewLine]", RowBox[{"f2", ":=", FractionBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"kb", " ", "\[Alpha]"}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], "-", FractionBox["\[Theta]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"\[Alpha]", " ", "\[Theta]"}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", FractionBox[ RowBox[{"2", " ", SqrtBox[ RowBox[{"kb", " ", RowBox[{"(", RowBox[{ RowBox[{"cv", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", RowBox[{"kb", " ", SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]]}], RowBox[{ FractionBox["1", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox["\[Alpha]", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]]}]}], "Input",\ CellChangeTimes->{{3.859450205497529*^9, 3.859450229253463*^9}}, CellLabel->"In[18]:=",ExpressionUUID->"477ccb54-2cd6-4b07-8754-a165b5188c10"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"pf3", "=", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"f1", ",", "f2"}], "}"}], ",", RowBox[{"{", RowBox[{"\[Alpha]", ",", "0", ",", "0.8"}], "}"}], ",", RowBox[{"Filling", "\[Rule]", RowBox[{"{", RowBox[{"1", "\[Rule]", "\[IndentingNewLine]", RowBox[{"{", "2", "}"}]}], "}"}]}], ",", RowBox[{"GridLines", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", "0.8", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.859450265037191*^9, 3.859450282953124*^9}}, CellLabel->"In[26]:=",ExpressionUUID->"3569b35b-238b-47e3-83b8-92517f4f2c3e"], Cell[BoxData[ GraphicsBox[{GraphicsComplexBox[CompressedData[" 1:eJxFl3c81e/7x60UURIZURlFUilSSq63UZEKhfAxU1HpOGSErGNFRlkle++9 ycoopIRSUtkcolApq+/9/j1+7+Ov83g97vtc9/W+rtc9nkJXrC9eY6Cjo+ul p6PDf5MmK+06/LQUZGX+uofLkrHXzIaVt7keglh6hxPvETLGNXheP6ghAU7U dplsliFjNoejh9eNZkAd36upXGkytsPuwfQb6wLYNTegP470oo3Zv5zGEhBb Xm3+iubn7d3EG91RAccUPtn4oPiXmbpP8x2ogZTAoNaDcmQs+j7PNq6aetCU nFxtlidjC1NSbKK1z+HBvlsTmxVRPqa67Pcmm+Ab9pvz3Wky9ujw+KP+2RZQ Pbo31fA8GSPHNtqs+/4SeJl3GU5rk7E2vhxDB552SClhcg0yJmMc8//avvN3 AKuXwsiiJRl7+9lEpVDtDeSpPvCkcyBjvQU+gYLlnaAR2Popz5uMyQs9qhgr ewv+Z+8yyIWTMaOnwpOXXnWBG4cKx5l0Mvar4YbRqTfdcLTtfJtmNRlTn5N9 3zfeA5/+zo2WdZOxA98z72kvvQNZC1a+1Bky5vu06+rF5fdwenQjlsdqg8Vc 8Lz4k/MDbJFTuBAiaYOJF4568vN8BD/dII8WDRtMaeD7F9FtfRBfdurHkr0N xsfrodgt8Qm6dnNtWUi2wSxWm0fX7e8Hu6zRpMBuG+zO9KOQfpXPcHBbzP56 NluMLZPR4vHlLxBlZmx6RN0W49+6z+P95a/A/x7rKHpgi80rWb3plx2A5iJm /YMfbbHw7lj3hxUDoKPNt+nq3jvYvbNJp8uODoK1RGvdcY87WGPzDY68hkE4 YhubVzFxBzvFy7ZkoTQEsdclEle07bDd1jYT8x1DsCzwKzSq1w7DYgt/K2oO Q9yustRIE3ssqbBpO0PnMEix+TzrmLfHzNueKocbjID1t98s99MdMJMq9cCJ TyMgueT+/am5I1aVV9e7yXIUjGKaYpdU72KG/szH02dHQWueW05W1QmTOyFe Q287BvahDTpJOs6Y3Syb8oGVMXjw2diYIckFm3R7RRVwH4dDZvcV2Ne5Yulz xumuq+OgvtoiKRPmhjXeLLEouD8BrW92vbZT9sD4q0ZUU1mocFblfZDNJU9s oOjdw6goKqiLRHC6VFEw/i8f3pK4PCBuz8h0C9oPLiNLR5ran4AsuzSjB/L3 c3+7OLXuFFD2SK9pR/7XZdf/enEoB9TlHn8rQ5rtjoNDbVQR8G/UunwWze/p KN+Y8rIM+Ccky5+ieAyPyQf7VqogWP8C17OjZKyF1bNyl3YdlPd9e9F3nIyp HRfdElPTAJUbtkS8UiBjV9Ia2TR7GuFFq21auzIZK2iN05CcaYYSHn+mn2pk zFX2s1W8FhX2fdWIbl/1xAoDuxhsuMjAMu4yvhftv5Rf2Qu85HA4yrzT9AXK 59aRQZdbbUngomQ/PYHyHdnpbJYznAVfjb88xvd3xDzd4RfehRDLYZbLieaP xwf6iLeUwpCH4tWjKH8907rkqtFKEJS/rc6H8g9eL0EnqFgLmcfqb6+g/W07 GLtV72QDqKqpfWw4ScYk1ZzZjqs1QtjLojNXlcgYRDgf0LZqhvV0Qz7/qZKx c38GDJL2U+Fy/6CcTLon9sleVTh1x31IaImqvoXWu9itbmctFgu3J1qfKqF8 +L+sbxDrT4PdHXn0FSjf1sWjRn8H8qDptpRAG9Jec1NVpXnF4J0uFRuM5jcs DT3a2V4O9h3iyyyoHjkdQtV/uZ9BF/NNIdIxMvaP2UouVLoe/CqaD748gc4v u49uMfZU2Bi87qeDAQX7Sm2+as9lCh+iDZWM0f/lVr30lJVCIc34dcUMio89 eHxzuTkRNhcY0i+h9SUyA4T1RzLB+0xfSA7SfdItIeqLBWB8RsAVH/+xwfH5 pEopmBvqCLOi72NsHvucpV8JM8G/fTpQ/DkfN5Ho8hoQ+KCRFY7qyVzaxyW7 Ug87aku4lFA9Q5/qsOUzNsLu1PracnReMrtMCFrua4bPCx84Is+QMemPQ2+T t1PhZHAze/89T2wxk2PRn88bbvw7rf8ErTf2SeRd1N+n4GI4xmaK8p+Rrs2v 6E2FzFucefUoPw5v1R1pg7mgpNd3qg7pl4cLeY+LFoMzq+HQTTS/7WrH60G1 clj45dPbieJdPqz2i+pfDT2O85JbUT2vBEpGJn2ug1q3CDsNVM9InU+/Ys2p 8LKLGscvScE4prsjZ2IjQbI82iEJxYv8KhHU9zoZzk7ul/iI1ouNvJHwbygb ROQ3sBYirVl8okdpcxFwLpyYl0Tza9rubD2lEw/K29eViCF9+r5WV+RAOmhl varF51NsxGLODeRD5bkNDr1IvwjrXR/tR4WRgVkzqj8Fk0/JEXfj0gSxJ8K7 nVC9vRl+3Nfb9wh6NxWeY0TfI1E2N9iknAgxZmnjTCj+62lOr/yrmWDbWzaL 93O5O6OWvbQACjSvsc4ibX/y24A6Uyn8yv7++Cear+e4uJi0tRKKLc2ZM1F8 0WbxI3226P67pFJrhvrZucOJe/fnetDqDwpnRP1UUVYOpA48BxZ9LgVz1M/J 2/Hcc6zNUBVXw3gE9TOt1TwohRPtb26+QBZLT4y16ee15W0USO1nuZaP8pUa CFmXPxQF1eZ/yq3R+h+M+cQ8dVKBR/wTtRnlV/yy023ZLBdKypZbq5Ce7Ao7 s/ylCF4L3zpqgOZrRClNK7GUg4jeeYtSFC9nxJBzSLka4rh7do+j/R3e/j59 8EkdlB4VieVC/WQ9bVgYZ0AF/105S1rcFMxgFl4w+kWAkzlLbAmK58Hqy5R8 Lhnoh/9rGEDrYZ9m6XTNsyF8+SxjPtK2l3YwrmsrBAs2zts70fwNb74qGyjE gbqO/zsZpKWKc9RMjNPhxVR6aAmav6csfznJNB+eR6jc7UT6uLdeY7QbFXpa knrZbCmYrqn8vLRqEtTdKMvF++F3leE5w9UsyP652IL3qyJs2NQfCsFbgbuY GcVnYjE/9kM/DfZ1cG98hsatoL5GwywPXByXTZuQzil5w82plQIjM/niXfj7 RmsQMq/kAKvPl5xipA2Nfhu8vpIBjoFUX/x7tJN1zz19SAXtpAvV7EkU7Dev c0EIFwZiuRGNvqj/mUx7hIbjH4JS/u5OdlTfePUEwUyGRNhyMnALK8pnF8fl 4j7RTLBKbPkPP3/ZRfnfk0ILwLtsmu8bnn/vHvLycAnIZC3wTKL5XpreLPE/ KsD4SdeOxyh+7chKjZNmDazL3pqqivxVdullhEBHPSi7uuWMoPdVHM/xV75v noOt29/bcshfhuPOW8oXm8A5b2ycCflrQFF0SnQTFTQ2NJ4tM/LEON+ORZdy e8KI1he+apSv7lBzrNzlKDjbFtfqiNY//7PlyjWuVPhp3FH/EuXHNMWVLyac Czvy/V7g5/GS8DoTo2dFcGqQ68BFND9U2vXe/EQZ7MxVW0hH8XprxnZ92VUN 0WF33N4if+2fypbydKgDh07d0AV0/6nUCmzeqUuFRB5qGDMrBXOftzcJXgqH AQ72qRoU73e8NOa3MRnirvU2jaD1QleOHPIUyQbZbUeP5yHtnRzCfz29EF6U uvzkRfP3v+XuHymKhU7f+uQTSKeqGvgoC6bDk7QuWfy+vvthXvL1rnxof7BF tgNpu2VeIQFn9B4YVBaRu07B2n9RD/CuT4Illr2nfqPxD76n5/aLZoFcisIT 3F+tw9p3JwUKYdo1/h8diu8Ux2HXw5sG0cwktVo0XmvGNOMslAePNzjUNSAt dNZV6/fmFHgTlRP5DulzdrvJPcI5IJU/fKYI6bdzyZFFQhkQpqIRUoB08Hae LP5AKnDr/PGci6Bg99pfX/ROyQSQLc3F1zdvvTUVE5kKR3uoxxql8fdC4IW3 iblg0Lj5J+7vmYrcTonkbPBeLz2P+7Va8B+7S3w6jHGpcuN+llWqfdSbnAV+ P8QEcP9lHIzd7JaUA52zW+RKkR57obpzMjkD2E6UpuL15d8XOcMXQQWRdCaZ E3kU7CYDd30RlxSIxLLGBSE/PluneFvc4CFYz8rs2or6bbDN8cT2oQR0f4uW sKH6qAo5qf9gyoSPB9ji8fW2veoy2+lZAIbc/cVUpD+KNpX3dJeA7emT1BE0 n/dkK4fg1wpw12BWDEbxA+wsKWpQA9h87EF55Hfxme86vM31EHHe4sI75Pc2 zyNW71qeAz3zSKIo8jt3imVI1FwTWASF//yGeGLFlYl/dCMVIgIogqF6nlhk 71dZzggPMLy8/K8e5Ws5PEB12xIF0/NWgy74+VQX69E7nwLH6d2P4++L/cuy Z04y5ELo3V3vynH/t9dMsmcXAX3/FfkLaH6xB39T+4cyEDDBtBJRPKusfeKG m6thvcKzhhbk90Xnbb80r9WBygXe3VTkd9PF5ZNfL1Hh+7H2jRZMFCz058Ps 7tJwGF0uTXiO4hXcZDX+O5kEoyFePWN4/zbptUYyZoPFsMwIXr9AddW0bZGF YMTV0MaNv0e6pMQlbsfCTK0kPyBtuvVQculyGqiJWPHg+SZQuZuH6fJh2Ig3 BX+/Pjr2V6PfEflrRPmzjikF862vPxcwlgjhkBP3B43TP7EMUGbKAjUG5f97 z3Q9YGeK3lgIk0WKx1aRlrkx/uj0n1R4ePqPA/5eGLfd4/uQPg/238lxxd8T /Vza1pbfk0HvWO1/+H1s53NmwyRDDvyM3pqC39eBNc4lovQZkBMjKYzrrMsL H/r8qSC8JFY4FULBUvt/TEZ5Z4JH5Vwbvv6OcCWWzQ6pkPA2IRA/rwPK88bG PHPh0QhHXzXSPG1vLDGvbPCZvuKA+91h4t2+abd0KN0o+Ab3u/Glgb3TXlnA 97bhGx7vLVaXHkbJgaLwzST8vkkM3XnS0CsDyp9abMH/f9TCQbAvlAp2fnr7 hTMo2MKqzPZmlUzQc18Vwut/49vWqFvK2XCfayIK3x8F9qIGvCpZ8FmpMwuP v0284y6mlAGJvUeZ8f18qSqnitSUCaYm9E/xcfZDMX8bGrNA30pKB48nuWJD f7cpA/H4O2U83spMaZ3+YyooFO/u0SuhYAS/Tz27O94UR6LxOzt1LNEUaYLf dbvfLMvGk2j8Tv+h7cuZRBKN36/NVwnFpJBo/N5V4niwI5NE43cRm4vpWAGJ xu8x08XFopUkGr9vpvM+9KuRRON3e8mVVY5OEo3fn5XJhEd+JdH4/d/gwg6v HyQav39m1hYLY7Sm8bvjWMe84nZrGr+rHttmZiljTeP3M/8SE9UuWdP4Xd3K sTzC3prG77l2KZrkKGsavzeI/nGearKm8fstSPh0aM6axu9C0m7RN7nW+D3F fVni4uE1fjd7ZR56XItM43c570g/bQcyjd+zB7RNMmLINH5fkTz9m7GFTON3 /9QiId8FMo3fn49yXfeUWON3dlXL3Z4WNjR+7wpSHHqdaUPjd0cTGfeVaRsa v9+cWa/5BNb4fWmIy6U+zJbG785CClwPZ2xp/F4tf9PV6b81fpfhO7e80H6H xu9Tzj2/lS+t8bvqbfHXVV/taPw+nn+E2+ruGr8v5Hy4wH9ojd/rmlOLh2Yd aPx+u2ss2q7fkcbvj2ocFz4P3KXxe+tJi45D8040fu+tjgj7pbLG7w6653h4 c+/R+L0kS4LzLLbG70/Xddx/LrDG74aU3L+XD67x+0XXx/rnotb4/aysnhMZ 7QeC38OzQvgTkCb4Pc1dg29bAonG7ycHgjhfJJFo/L79Usf3lTQSjd8NHNap dOeQaPwesLBnlFxCovE7vaArk2oticbvaQUXBZ+3kmh8vv7ltqE9/Wt8TrrJ oRqK8iH4XNQhONseaYLPk5j9bsSg/Uvw+Uu/itlltH8JPj8nsSm5LpVE43Pb xdYQ5WwSjc919/+Xo1pEovF55QV7l9RqEo3PD4h2VrS3kGj8beIn+a3Ha42/ GR+PvjFB+RD8bfXD0HwAaYK/5a/32qag+hH8HZ1Sk5mWTKLx9/SA1JPLGSQa f3Pv1Wy/l0ei8XUvUyxv0LE1vgbxCUomik/wtc1fBU9LpAm+nvbZdcgC1YPg 67n9f17Fo3oQfM3X3f9IAtWD4Ov9BivyPlkkGl+vZEvlYYUkGl//fBk6aVpF ovG1dbOBl2EzicbPj/5rC92pv8bPmcsxi9dQPgQ/J7YY3atBmuDnO72GWQao HgQ/612rE5dB9SD4WWfJUiM9nUTj503RJ5tTckk0Ppb+W6nezULBbEWVLqXv uAvxNsaK7ig+wctevyUO3kea4GW/jVlF71E9nil6nK0XCQSvDCYmYzRO8PH9 XJcvG9A4wb9UTcfNRpZr/LuwP76gDM0n+HfnBA/VHGmCfx0zFBwvoP8T/Luz /9PBO6jeBP8e4G/yHUL3B8G/qlUBJHFUb4J/NbgP5tah+4Pg32pnleYGdH8Q /LuuUfprehOJxrefSxY9d6is8e3x03sKbqJ8CL6V/luzPQ9pgm8Fn1ZWH0X1 Jvi2ME9odhntX4JvncqjG7VQvQm+3XCM5cgJVG+CX81tZec/zXlioXqs+wL5 7ODrt4CTeH0Jns07dU7RDWmCZ7l1j0xVoHq8+u9q2WGhAMgQtjLC603wq+U3 x+l5pAk+/fwlolZLk4IleB4pzd5hCVt+xZnE4n75yyN+QD8M+LVErEhIT4ZI BvMI+EI3xmVwBemY3vIUb44YYJRXU3iN9KUfTi7PRe5BsEe/tiPSLRMW1z+W PAYpgSWHMKRzxGK+nN8TDM8esjfj+RA8misWIF3gscajNmrLWbhfCR69weC6 HV+P4NHYiUOhSuj7CB51tJoyMkL9JnjUtiBhZx3qN8GjT1RkYhfRe4Hg0fZu 5il31G+CR22cpRZtUb8JHo3vKVa7gPpN8Kb34aXFYrk13nzz2MT2NsqH4M3r krrf05AmeJPHmqdhD+o3wZtPGN6+H0T9JngzTvFjkhjqN8Gb+9wbNqxH/SZ4 8oqcx2GncU8syXYmcnWbLfCH8wgFofgEX2pI+7Y7IU3w5R1qrWcWqkePpe63 qZ3+kHMnZh6vL8GTlveyl6hIE7zoIOyZcV2FgtWXrgQ+5LsKqhyDGsn4e2z5 fH1FRyisn5M/dwvpuZgdTZ38PuC4mrT+KtINH6flN/tEg4cWW2Ez0ldYjcdl hJzB/x/nXhekpyZjV833PoZXleXpeL4lMsFc63cHgTHfbkU8H4IPv/rphLva UTBjuqofHWWPQFTtB+t1NM5QziClzOsFPTy9h/HzlKKwp45PwAG+u4fHeiF9 5DvLQSfOSPjuy8+O66YLth5Owg8gU82DHY/fujAYkjwSBgcN9g3aID1EOa5n LOgHsvQCc/h7M4U/KyNcLAQ8BCdD8PuC4MP5POGtvwLX+PDuvr9YAxon+DB3 VEbbDN9v/8+H5IzgGnlUb4IPM7WZwi8i/xF8eNY1ICwX+Y/gw/HYsY/DyH8E H2o4mcuZIv8RfLj3+dUWdeQ/gg/b6n7nCiH/Efx3YIPZPm+ZNf57l3l6Gt+P BP+p2zA44/0j+I/O+tOVHch/BP85sM/e6EH+I/jvPUtiNSfyH8F/m1kd+KbR e4HguyeVOqsdg55YlvvAq3JuG9jOtzcnBMUneO/wnp4CfH8TvMen63YrGdVD z1rDTzX+Ppim0Onj9SX4LkJeT3QUaYLfnvCyFTkqULDON4N/GHiugEjkJjN8 /+xZsWRb9QuFHBfR/htIOyTzmOx/6g0XVe3/4P7r6dvgrw3RsPwn7QHen5s8 moIzO51Arr5C0hXp1amKs5nDkTC0N24gAOljJ/zyzVMCgSWhlg/3B8Fr4dp/ OG6RKJgN/Tv5rTaP4H3/3e94fN+apbb4x+g8f/bFEl8/QJ33Vxe/Pdid5x/1 QVr1h6hL7asIuNJAivHAtc6t7e8TA6B1KksSj9//Z/nTRFwYVAb8246/5677 S89XxfiCZcyVWNw/4kLJyrNpwXA39KkQXh+C1zbNjOh1+lKwSMaN72JHH0K6 VssCft5pXjHSCknwByHH2ng8Pily9167aB+47L1PHL//pA5EOGWlBsGPsJPO +Dim6jQqkPwAtpXO/jNC2vieYg19nB/M953Sw/2/i6uQ/VhGCHSU03PgmuA1 uU5uix1hFOx/PoMATQ== "], {{{}, {}, {}, {}, {}, {}, {}, {RGBColor[0.368417, 0.506779, 0.709798], Opacity[0.2], EdgeForm[None], GraphicsGroupBox[PolygonBox[CompressedData[" 1:eJwl1VOUHgYQBtDd2LY3Nhrb9sZONtZubNu2nbaxbdspkjJp47RJ3aC9/9mH O9/rnDNnZkLCIkLDowQFBQXzhfJBfirH0IFanGAxQyjJIebSj0uspRVnWM4I CrCbafTkImtozCmWcpthXGMj96jMURZwi4FcYT13acs5VnKHUVxnE/f5qP/P 5FhuEsYFVlObkyxhKFfZQCkOM4/+XGYdrTnLCkZSkD1MpxdNOM0yhlOFYyxk EO34Tz+fy3F0pA6lOcJ8BtCGQuxlBr1pStXgyMFsYTydqEsZPmEfMwmnGdUI ZisT6Ew9ylKY/cwiguZUJwrbmEgX6lOOIhxgNn1oQQ2isp1JdKUB5SlKNHYw mW40pALFiM5OptCdUCpSnBjEJBaxiUNc4hGfBCQkEYlJQlKSkZwUpCQVqUlD WtKRngxkJBMhZCYLWclGdnKQk1zkJg95yccuptKDRlSiBAeZQ19aUpPjLGIw 7TnPKkZzg83BkXuWPzBD433POX5nEUd5QR9msocfaUQ3JrKFrylHLdoxgnXc ohAFKUB+8pGXPOQmFznJQXaykZUsZCaETGQkA+lJR1rSkJpUpCQFyUlGUpKQ mEQkJAHxiUdZatKW4azlJnEpQw3aMIw13CAOpalOa4aymuvEJpSuTAjsGV9R imq0YgiruEYsGtKF8YE7wZeUpCotGcxKrhKTBnRmXOAuBm4kJahCCwaxgivE oD6dGMtm7lOcXkxlB99SmTns5yeaM5DlXCY6EcxgNz9Qj3kc5AkdOcFrxrCJ exTjDG9ZwGGe0ZOT/MIU/mQ731CJfznNG2bzF/t4TDP+4RgvGcAfLOMS0XjH WX5jIX9zhOeEc4pfmc4uvqcucznAz4RxnFeMZiN3Kcp8DvGUHkxmGw+pyCz2 8oim9GcpF4lKb6axk++oQwdGsYE7FKE7k9jKAyrQhH4s4QKBn1mb9oxkPbcp THka05fFnA+K/K//Aw883Zo= "]]]}, {}, {}}, {{}, {}, {}, TagBox[ {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[1.], LineBox[{1, 198, 151, 113, 84, 63, 51, 210, 163, 125, 96, 75, 2, 199, 152, 114, 85, 64, 219, 172, 134, 105, 52, 211, 164, 126, 97, 76, 223, 176, 138, 109, 3, 200, 153, 115, 86, 227, 180, 142, 65, 220, 173, 135, 106, 232, 185, 147, 53, 212, 165, 127, 237, 190, 98, 230, 183, 145, 77, 224, 177, 139, 240, 193, 110, 234, 187, 248, 149, 243, 196, 251, 4, 201, 154, 245, 116, 236, 189, 249, 87, 228, 181, 247, 143, 241, 194, 250, 66, 221, 174, 246, 136, 239, 192, 107, 233, 186, 148, 242, 195, 54, 213, 166, 128, 238, 191, 99, 231, 184, 146, 78, 225, 178, 140, 111, 5, 202, 155, 117, 88, 229, 182, 144, 67, 222, 175, 137, 108, 55, 214, 167, 129, 100, 79, 6, 203, 156, 118, 89, 68, 56, 215, 168, 130, 101, 80, 7, 204, 157, 119, 90, 69, 57, 216, 169, 131, 102, 81, 8, 205, 158, 120, 91, 70, 58, 217, 170, 132, 103, 82, 9, 206, 159, 121, 92, 71, 59, 10, 207, 160, 122, 93, 72, 60, 11, 208, 161, 123, 94, 73, 61, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 209, 162, 124, 95, 74, 62, 218, 171, 133, 104, 83, 226, 179, 141, 112, 235, 188, 150, 244, 197, 252, 50}]}, Annotation[#, "Charting`Private`Tag$10689#1"]& ], TagBox[ {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[1.], LineBox[CompressedData[" 1:eJwV0dVSFQAABNCL3d19RRS7O7AVFVRUsAM7EREbBWyxULG7u7sLRbHzwW8R PTyc2dm3ndlgfELMgpBAIPCHv5xXUpnCIJ6xj2V05gGZLOIdJxjHKw6xipbc ZAtzyeE4I3nBAb6xgo+c4Sd9eMwevpJMLqf4wUSyOcJ3VvOJs/wiz/4LMo0v xPOWYwzmOftZzgdO04WH7CKJ95xkPK85TAqtuEUG8xjFSw6ykr48IYslTOKf PRdlOlMZQlcesZvFTKA1t9nKfGLpl38Kl1jLNKLoRhvusI388+LoTwiXWcd0 oulOW+6ynQRGM4ACXGE9MxhKD9pxjx0sZAwDKchVNjCTYUTQnkJcYyOzGE5P OlCY62xiNjH0oiNFKEoxilOCkpSiNGUoSznKU4GKVKIyVahKNapTg5rUojZ1 qEs9gtQnlAaE0ZBGhNOYJjSlGc25wWbmMILedOI+O0lkLJE8ZS9LmcwbjrKG z5zjNy34DwIjYRU= "]]}, Annotation[#, "Charting`Private`Tag$10689#2"]& ]}}], {}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0, 244.9489745827529}, DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{{0.8}, {}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImagePadding->All, Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& ), "CopiedValueFunction" -> ({ (Identity[#]& )[ Part[#, 1]], (Identity[#]& )[ Part[#, 2]]}& )}, "AxesInFront" -> True}, PlotRange->{{0, 0.8}, {244.9489745827529, 599.3100940371891}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.859450273820162*^9, 3.8594502840725183`*^9}}, CellLabel->"Out[26]=",ExpressionUUID->"ef277ec8-c3ed-40e2-a079-00ac61871d75"] }, Open ]], Cell["\<\ The profit: \ \>", "Text", CellChangeTimes->{{3.859450343337944*^9, 3.859450349473587*^9}},ExpressionUUID->"43d0af90-9d39-4132-b8aa-\ 127df6bd34a5"], Cell[BoxData[{ RowBox[{"eb", ":=", StyleBox[ FractionBox[ RowBox[{"pb", "-", RowBox[{"pb", " ", "\[Alpha]"}], "+", "\[Theta]"}], RowBox[{"2", " ", "kb"}]], FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]", RowBox[{"pb", ":=", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "\[IndentingNewLine]", RowBox[{"rb", ":=", " ", RowBox[{"1", "-", "eb"}]}], "\[IndentingNewLine]", RowBox[{"Profitvb", ":=", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", RowBox[{"eb", " ", RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], "\[Theta]"}], "-", RowBox[{"kb", "*", RowBox[{"(", RowBox[{"eb", "*", "eb"}], ")"}]}], "-", "cv"}]}], "\[IndentingNewLine]", RowBox[{"Profitib", ":=", RowBox[{ RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}]}]}], "\[IndentingNewLine]", RowBox[{"Profitsb", ":=", RowBox[{ RowBox[{ RowBox[{"-", "\[Alpha]"}], " ", "pb"}], "+", RowBox[{"eb", RowBox[{"(", RowBox[{"f", "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}]}], ")"}]}], "-", "cs", " ", "-", RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", "csb", "-", "cvb"}]}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.85945039225144*^9, 3.859450418973852*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"e12ca16f-e2c7-4c3a-a490-861d6ad6312d"], Cell[CellGroupData[{ Cell[BoxData["eb"], "Input", CellChangeTimes->{{3.85945044020502*^9, 3.8594504437198133`*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"413edbb3-dfd3-4fba-beac-8cb9d86e0e14"], Cell[BoxData[ FractionBox[ RowBox[{"\[Theta]", "+", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], RowBox[{"2", " ", "kb"}]]], "Output", CellChangeTimes->{3.859450444480567*^9}, CellLabel->"Out[7]=",ExpressionUUID->"a0770297-1cba-49ee-853a-19a2a24847ec"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", FractionBox[ RowBox[{"\[Theta]", "+", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], RowBox[{"2", " ", "kb"}]], "]"}]], "Input", NumberMarks->False, CellLabel->"In[8]:=",ExpressionUUID->"236dd620-81bc-4c73-8ab8-352e324cfef7"], Cell[BoxData[ RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ FractionBox["f", "kb"], "+", FractionBox[ RowBox[{"2", " ", "\[Alpha]"}], RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "+", FractionBox["\[Theta]", "kb"]}], ")"}]}]], "Output", CellChangeTimes->{3.859450450442974*^9}, CellLabel->"Out[8]=",ExpressionUUID->"20d3dc67-b786-4161-977c-383822d66457"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["rb"], "Input", CellChangeTimes->{{3.8594504537263203`*^9, 3.859450454793315*^9}}, CellLabel->"In[9]:=",ExpressionUUID->"247dbbd5-49dd-4872-9ced-87df9305dc76"], Cell[BoxData[ RowBox[{"1", "-", FractionBox[ RowBox[{"\[Theta]", "+", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], RowBox[{"2", " ", "kb"}]]}]], "Output", CellChangeTimes->{3.859450455272242*^9}, CellLabel->"Out[9]=",ExpressionUUID->"0a8d8cc6-8195-4a1a-ac9d-f8911bf58051"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{"1", "-", FractionBox[ RowBox[{"\[Theta]", "+", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], RowBox[{"2", " ", "kb"}]]}], "]"}]], "Input", NumberMarks->False, CellLabel->"In[10]:=",ExpressionUUID->"b5e9896f-cc8a-4267-90d4-d7bde5fad96c"], Cell[BoxData[ FractionBox[ RowBox[{"f", "+", RowBox[{"2", " ", "kb", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "\[Alpha]"}], ")"}]}], "-", RowBox[{"f", " ", "\[Alpha]"}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"4", " ", "kb", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]]], "Output", CellChangeTimes->{3.859450457272696*^9}, CellLabel->"Out[10]=",ExpressionUUID->"fff47a49-e9fb-4833-8ad1-817c07083073"] }, Open ]], Cell[BoxData[{ RowBox[{"rb", ":=", RowBox[{"1", "+", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"2", " ", "\[Alpha]"}], RowBox[{"1", "-", "\[Alpha]"}]], "-", FractionBox[ RowBox[{"f", "+", "\[Theta]"}], "kb"]}], ")"}]}]}]}], "\[IndentingNewLine]", RowBox[{"eb", ":=", StyleBox[ RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"f", "+", "\[Theta]"}], "kb"], "-", FractionBox[ RowBox[{"2", " ", "\[Alpha]"}], RowBox[{"1", "-", "\[Alpha]"}]]}], ")"}]}], FontColor->RGBColor[1, 0, 0]]}], "\[IndentingNewLine]", RowBox[{"pb", ":=", FractionBox[ RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "\[IndentingNewLine]", RowBox[{"Profitsb", ":=", RowBox[{ RowBox[{ RowBox[{"-", "\[Alpha]"}], " ", "pb"}], "+", RowBox[{"eb", RowBox[{"(", RowBox[{"f", "-", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], "pb"}]}], ")"}]}], "-", "cs", " ", "-", RowBox[{"rb", RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "eb"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{"\[Alpha]", " ", "pb"}], "+", "cs", "+", "f"}], ")"}]}], "-", "csb", "-", "cvb"}]}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.859450469486827*^9, 3.85945047110107*^9}, { 3.859450526077877*^9, 3.859450554793116*^9}}, CellLabel->"In[11]:=",ExpressionUUID->"4afa4a7c-a015-44f1-a0dd-0c2b59a8b030"], Cell[CellGroupData[{ Cell[BoxData["Profitsb"], "Input", CellChangeTimes->{{3.859450559342915*^9, 3.8594505639133463`*^9}}, CellLabel->"In[15]:=",ExpressionUUID->"9d7961c0-e316-4661-87bc-4f683b4b6ccf"], Cell[BoxData[ RowBox[{ RowBox[{"-", "cs"}], "-", "csb", "-", "cvb", "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"2", " ", "\[Alpha]"}], RowBox[{"1", "-", "\[Alpha]"}]]}], "+", FractionBox[ RowBox[{"f", "+", "\[Theta]"}], "kb"]}], ")"}], " ", RowBox[{"(", RowBox[{"f", "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], ")"}]}]}]], "Output", CellChangeTimes->{3.859450564844936*^9}, CellLabel->"Out[15]=",ExpressionUUID->"6e6bdafc-e900-42dc-b25f-bd4b0543b6a3"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{ RowBox[{"-", "cs"}], "-", "csb", "-", "cvb", "-", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "+", RowBox[{ FractionBox["1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"2", " ", "\[Alpha]"}], RowBox[{"1", "-", "\[Alpha]"}]]}], "+", FractionBox[ RowBox[{"f", "+", "\[Theta]"}], "kb"]}], ")"}], " ", RowBox[{"(", RowBox[{"f", "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "-", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "-", "\[Theta]", "+", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], ")"}]}]}], "]"}]], "Input", NumberMarks->False, CellLabel->"In[16]:=",ExpressionUUID->"006e0b67-118d-4028-aa8a-413b45e87bbc"], Cell[BoxData[ RowBox[{ RowBox[{"-", "cs"}], "-", "csb", "-", "cvb", "+", FractionBox[ RowBox[{"\[Alpha]", " ", RowBox[{"(", RowBox[{ RowBox[{"f", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"f", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", "\[Theta]"}]}], ")"}], " ", RowBox[{"(", RowBox[{"f", "-", RowBox[{"f", " ", "\[Alpha]"}], "+", RowBox[{"2", " ", "kb", " ", "\[Alpha]"}], "+", "\[Theta]", "-", RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}], RowBox[{"8", " ", "kb", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]], "Output", CellChangeTimes->{3.8594505734341383`*^9}, CellLabel->"Out[16]=",ExpressionUUID->"db31caeb-478f-4d48-9e27-8972d2fa0663"] }, Open ]], Cell[BoxData[""], "Input",ExpressionUUID->"80741104-ee07-4254-a638-ff09180b02e1"] }, Open ]] }, WindowSize->{714, 730}, WindowMargins->{{Automatic, -40}, {Automatic, 16}}, FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) \ (2020\:5e743\:670813\:65e5)", StyleDefinitions->"Default.nb", ExpressionUUID->"75f94076-023f-430a-a1f8-98ac57dee0b9" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 330, 8, 130, "Text",ExpressionUUID->"8da70118-74ed-4ef1-86e6-26d1ad97f2f4"], Cell[891, 30, 1898, 54, 94, "Input",ExpressionUUID->"06fa2129-7c21-4d8b-a4e6-74232a429dd9"], Cell[CellGroupData[{ Cell[2814, 88, 229, 4, 44, "Input",ExpressionUUID->"9907c7dd-e61f-4f2c-b9f6-bedf58db12e4"], Cell[3046, 94, 321, 8, 34, "Output",ExpressionUUID->"ed2c5394-980c-43ea-a6d5-499bc8710fec"] }, Open ]], Cell[CellGroupData[{ Cell[3404, 107, 259, 5, 44, "Input",ExpressionUUID->"e4d26ebd-3078-4e62-8ebd-aa5b21fb3b60"], Cell[3666, 114, 353, 9, 52, "Output",ExpressionUUID->"045c1f00-27a8-472e-8e3f-59be3f6a17a7"] }, Open ]], Cell[4034, 126, 882, 25, 131, "Text",ExpressionUUID->"5dfded16-bb8c-4e5b-9705-0033db33afac"], Cell[4919, 153, 318, 7, 49, "Input",ExpressionUUID->"1edb5d18-7f61-46ca-b234-9aed4bf11240"], Cell[CellGroupData[{ Cell[5262, 164, 178, 2, 30, "Input",ExpressionUUID->"00f0560b-8850-4cfa-b12d-39a8e260b8c1"], Cell[5443, 168, 878, 26, 54, "Output",ExpressionUUID->"70037904-6240-4d0e-bb96-c5db95b09629"] }, Open ]], Cell[CellGroupData[{ Cell[6358, 199, 916, 27, 64, "Input",ExpressionUUID->"356391f7-c78a-491a-af2d-bb84c0b1fbbf"], Cell[7277, 228, 782, 23, 54, "Output",ExpressionUUID->"cf0f6104-b064-4192-ac24-a46cb7502d8c"] }, Open ]], Cell[CellGroupData[{ Cell[8096, 256, 355, 7, 44, "Input",ExpressionUUID->"7760dcc2-2bc2-448e-8c89-2717c75dc48e"], Cell[8454, 265, 1901, 50, 127, "Output",ExpressionUUID->"c00eb01c-76d5-4fc2-a07f-e522e1767a89"] }, Open ]], Cell[10370, 318, 1185, 31, 66, "Text",ExpressionUUID->"baf5aa37-09b4-413c-9689-23e912903e55"], Cell[11558, 351, 2976, 77, 281, "Text",ExpressionUUID->"cd4aa122-c8d1-455a-b063-43463770f7a2"], Cell[14537, 430, 491, 15, 30, "Input",ExpressionUUID->"d9b09ccc-4498-44c3-81ff-ab17d5a7d3d3"], Cell[CellGroupData[{ Cell[15053, 449, 340, 6, 44, "Input",ExpressionUUID->"4eb450a1-f7d3-47d5-acdd-f6aa6748565f"], Cell[15396, 457, 391, 10, 52, "Output",ExpressionUUID->"5c7992db-59bf-4242-8e46-1c2d13ec2f77"] }, Open ]], Cell[15802, 470, 152, 3, 30, InheritFromParent,ExpressionUUID->"d5bb36e8-fbe8-4b04-aa43-d72d323f6367"], Cell[CellGroupData[{ Cell[15979, 477, 350, 5, 56, "Subsubsection",ExpressionUUID->"100ae43e-10c0-4da8-b44d-0c7d244eac83"], Cell[16332, 484, 1271, 37, 134, "Input",ExpressionUUID->"63b57c6a-6890-4163-a939-1e97c2548b22"], Cell[CellGroupData[{ Cell[17628, 525, 179, 2, 30, "Input",ExpressionUUID->"dc9d14a8-dc93-44e7-9988-f16aa4bbf5a8"], Cell[17810, 529, 1249, 37, 92, "Output",ExpressionUUID->"a2d6fa11-cd66-4278-8ced-963a216a81a1"] }, Open ]], Cell[CellGroupData[{ Cell[19096, 571, 1246, 37, 105, "Input",ExpressionUUID->"9db77f90-bbef-4891-9547-982e77e080ac"], Cell[20345, 610, 933, 24, 75, "Output",ExpressionUUID->"3d9f6c75-9526-43a8-8de5-716065173c63"] }, Open ]], Cell[CellGroupData[{ Cell[21315, 639, 290, 6, 65, InheritFromParent,ExpressionUUID->"e5e300b9-8010-4af3-b52a-3fa809d8e524"], Cell[21608, 647, 598, 14, 54, "Output",ExpressionUUID->"fb6222d9-df24-4b40-aab1-eb87eb098b90"] }, Open ]], Cell[CellGroupData[{ Cell[22243, 666, 257, 5, 44, "Input",ExpressionUUID->"121c8452-1aca-47e5-a47a-1b31b7eecdb9"], Cell[22503, 673, 599, 16, 55, "Output",ExpressionUUID->"e1f49118-7f19-48dc-853a-f955feeda155"] }, Open ]], Cell[23117, 692, 1950, 59, 139, "Text",ExpressionUUID->"18005770-317f-4c40-a3a2-9474f3709773"], Cell[25070, 753, 1434, 39, 102, "Input",ExpressionUUID->"69075f88-39c0-49f6-91ca-c8d173fe15d9"], Cell[CellGroupData[{ Cell[26529, 796, 121, 1, 30, "Input",ExpressionUUID->"f8bad67e-6668-4273-a625-d80e056d081d"], Cell[26653, 799, 1229, 33, 102, "Output",ExpressionUUID->"36b30de3-7e6f-492d-abd7-3a8a3db339f1"] }, Open ]], Cell[CellGroupData[{ Cell[27919, 837, 1279, 35, 117, "Input",ExpressionUUID->"ac941077-927d-4535-91d8-07c3cbfb6f59"], Cell[29201, 874, 895, 25, 62, "Output",ExpressionUUID->"03126934-5ebe-4a85-80dc-0bae79be173e"] }, Open ]], Cell[CellGroupData[{ Cell[30133, 904, 259, 5, 44, "Input",ExpressionUUID->"334e5b24-49b5-4394-b491-699e9c900b5c"], Cell[30395, 911, 1915, 59, 82, "Output",ExpressionUUID->"6e22bbf4-7bcf-45e6-a3e6-d94d2f731d46"] }, Open ]], Cell[32325, 973, 3876, 122, 274, "Input",ExpressionUUID->"477ccb54-2cd6-4b07-8754-a165b5188c10"], Cell[CellGroupData[{ Cell[36226, 1099, 686, 18, 80, "Input",ExpressionUUID->"3569b35b-238b-47e3-83b8-92517f4f2c3e"], Cell[36915, 1119, 13341, 235, 237, "Output",ExpressionUUID->"ef277ec8-c3ed-40e2-a079-00ac61871d75"] }, Open ]], Cell[50271, 1357, 162, 6, 58, "Text",ExpressionUUID->"43d0af90-9d39-4132-b8aa-127df6bd34a5"], Cell[50436, 1365, 2263, 70, 223, "Input",ExpressionUUID->"e12ca16f-e2c7-4c3a-a490-861d6ad6312d"], Cell[CellGroupData[{ Cell[52724, 1439, 173, 2, 30, "Input",ExpressionUUID->"413edbb3-dfd3-4fba-beac-8cb9d86e0e14"], Cell[52900, 1443, 976, 27, 62, "Output",ExpressionUUID->"a0770297-1cba-49ee-853a-19a2a24847ec"] }, Open ]], Cell[CellGroupData[{ Cell[53913, 1475, 1013, 28, 72, "Input",ExpressionUUID->"236dd620-81bc-4c73-8ab8-352e324cfef7"], Cell[54929, 1505, 414, 12, 52, "Output",ExpressionUUID->"20d3dc67-b786-4161-977c-383822d66457"] }, Open ]], Cell[CellGroupData[{ Cell[55380, 1522, 174, 2, 30, "Input",ExpressionUUID->"247dbbd5-49dd-4872-9ced-87df9305dc76"], Cell[55557, 1526, 1023, 28, 62, "Output",ExpressionUUID->"0a8d8cc6-8195-4a1a-ac9d-f8911bf58051"] }, Open ]], Cell[CellGroupData[{ Cell[56617, 1559, 1062, 29, 72, "Input",ExpressionUUID->"b5e9896f-cc8a-4267-90d4-d7bde5fad96c"], Cell[57682, 1590, 524, 14, 53, "Output",ExpressionUUID->"fff47a49-e9fb-4833-8ad1-817c07083073"] }, Open ]], Cell[58221, 1607, 1935, 61, 201, "Input",ExpressionUUID->"4afa4a7c-a015-44f1-a0dd-0c2b59a8b030"], Cell[CellGroupData[{ Cell[60181, 1672, 181, 2, 30, "Input",ExpressionUUID->"9d7961c0-e316-4661-87bc-4f683b4b6ccf"], Cell[60365, 1676, 1436, 43, 100, "Output",ExpressionUUID->"6e6bdafc-e900-42dc-b25f-bd4b0543b6a3"] }, Open ]], Cell[CellGroupData[{ Cell[61838, 1724, 1486, 44, 113, "Input",ExpressionUUID->"006e0b67-118d-4028-aa8a-413b45e87bbc"], Cell[63327, 1770, 1439, 43, 100, "Output",ExpressionUUID->"db31caeb-478f-4d48-9e27-8972d2fa0663"] }, Open ]], Cell[64781, 1816, 81, 0, 30, "Input",ExpressionUUID->"80741104-ee07-4254-a638-ff09180b02e1"] }, Open ]] } ] *)