Consider the linear program minimize z=2x1-3x2 subject to 4x1+3x2<=12 x1-2x2<=2 x1, x2>=0 Represent the point x=(1,1)T as a convex comination of extreme points. (i) Draw graph of feasible region; show location of x (ii) Find 2 different convex combinations using 3 extreme points. (iii) Find a 3rd convex combination using all 4 extreme points. [Hint: find 3 different combinations of extreme points that surround the point you are trying to represent; remember that the coefficients must sum to one and be > 0]

Consider the linear program minimize z=2x1-3x2 subject to 4x1+3x2<=12 x1-2x2<=2 x1, x2>=0 Represent the point x=(1,1)T as a convex comination of extreme points. (i) Draw graph of feasible region; show location of x (ii) Find 2 different convex combinations using 3 extreme points. (iii) Find a 3rd convex combination using all 4 extreme points. [Hint: find 3 different combinations of extreme points that surround the point you are trying to represent; remember that the coefficients must sum to one and be > 0]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the linear program

minimize z=2x1-3x2

subject to 4x1+3x2<=12

x1-2x2<=2

x1, x2>=0

Represent the point x=(1,1)T as a convex comination of extreme points.

(i) Draw graph of feasible region; show location of x

(ii) Find 2 different convex combinations using 3 extreme points.

(iii) Find a 3rd convex combination using all 4 extreme points.

[Hint: find 3 different combinations of extreme points that surround the point you are trying to represent; remember that the coefficients must sum to one and be > 0]

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Step 2: Optimal solution for the given LPP

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Step 3: Mark the location of x

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Step 4: Evaluation of 2 different convex combinations using 3 extreme points

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Step 5: Evaluation of 3rd convex combination using all 4 extreme points

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