Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th...

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Let’s Make the 3D Graphics 18 th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

Transcript of Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th...

Page 1: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

Let’s Make the 3D Graphics

18th May, 2019

Gakushuin University, Faculty of Economics

Prof. Yukari SHIROTA

Page 2: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

3D Plot

Plot3D[ x^0.2 * y^0.6, {x, 0, 20}, {y, 0, 20}, PlotRange -> {0, 10}]

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3D Plot with other options

Plot3D[ x^0.2 * y^0.6, {x, 0, 20}, {y, 0, 20}, PlotRange -> {0, 10},

BoxRatios -> 1, PlotStyle -> {Opacity[0.7], Green},

AxesLabel -> {"Hamburger", "Orange squash", "Utility"},

ImageSize -> 200]

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Pallet for special characters from the menu

Page 5: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

Conduct the Lagrange method.Definition of Lagrange function:

F[x_,y_,λ_]:=x0.2 * y0.6+λ (M-(P1 x+P2 y));

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Partial differentiation

• Set of equations

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Conduct the Lagrange method.

We can get the 5 answers. We will use the first real number one.

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Select the first answer by First command

Page 9: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

Replace {x,y,u} by the first answer

Then pts definition

We will use the pts definition repeatedly.

Replace a variable with a value:

/.

pts:=0.25𝑀

P1,0.75𝑀

P2, 0.637712

𝑀

P1

0.2𝑀

P2

0.6

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Calculate intersection.

M=2900; P1=130; P2=170;

zvals=Table[{xx, (M/P2-xx*P1/P2), xx0.2 * (M/P2-xx*P1/P2)0.6}, {xx,0,20}]

This is the result.21 points

Let’s draw the points.

Page 11: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

Draw the 21 points.

M=2900;P1=130;P2=170;

zvals=Table[{xx,(M/P2-xx*P1/P2),xx0.2*(M/P2-xx*P1/P2)0.6}, {xx,0,20}]

ListPointPlot3D[zvals, PlotStyle->Red]

Page 12: Let’s Make the 3D Graphics20010570/MATHEMATICA/mathem… · Let’s Make the 3D Graphics 18th May, 2019 Gakushuin University, Faculty of Economics Prof. Yukari SHIROTA

ShowDisplay several items at the same time.

Show[AAAAAA,BBBBBB,CCCCCC]

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U’ s contour

From 0.5 to 20 by a step 0.1

• Given x and U

• Unknown y

𝑦 =𝑢𝑣𝑎𝑙

53

𝑥13

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U’ s contour• Maximum point

pts[[3]] is

Find the u’s contour curve

From 0.5 to 20 by a step 0.1

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Budget Restriction Plane &Maximum point noted by Arrow

Graphics3D[{Polygon[{{0,M/P2,0},{M/P1,0,0},{M/P1,0,10},{0,M/P2,10},{0,M/P2,0}}],

Arrow[{pts-{2,2,0}, pts}]]

2 graphics items

(1) Polygon

(2) Arrow

The arrow vector is set to be {2,2,0}.

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Plane &Arrow

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Manipulatesmall test

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Change M, P1 and P2 by using slidersManipulate

Repeated part

M with the initial value 3000 of which range is from 100 to 5000 by step 100

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Final combine of all parts

• Remove M=2900; P1=130; P2=170;so that the Manipulator can change the values

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Drill

• Change the target function to 𝑥 + 𝑦

• When you are making the drill program, please close the other manipulation program, because in Mathematica variables may be affected by other program variables.


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