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2 (a) Solve the following linear program graphically Identify the feasible region and the optimal solution. Plot the objective function as a double dashed line broken line (======) through the optimal point. Label the feasible extreme points starting with the feasible extreme point with coordinates closest to X1, X2] = [0, 0] as A, and continuing counter-clockwise for the other feasible extreme points. Minimize Z = 15 X1 - 15 X2 S. t. - 2X1 2 X1 2 X2 s 16 (1) 2 X2 s 16 X1 X2 < 15 X2 9 X1, X2 0 2 (b) Provide the optimal solution, X1, X2 and the optimal value of the objective function, L for problem 2 (a). 2 (c) For each feasible Extreme Point in Problem 2 (a), Complete the following table (add additional rows as needed): Point x1 x2 Optimal? (Y/N] Why? 0.0 0.0 0.0

2 (a) Solve the following linear program graphically Identify the feasible region and the optimal solution. Plot the objective function as a double dashed line broken line (======) through the optimal point. Label the feasible extreme points starting with the feasible extreme point with coordinates closest to X1, X2] = [0, 0] as A, and continuing counter-clockwise for the other feasible extreme points. Minimize Z = 15 X1 - 15 X2 S. t. - 2X1 2 X1 2 X2 s 16 (1) 2 X2 s 16 X1 X2 < 15 X2 9 X1, X2 0 2 (b) Provide the optimal solution, X1, X2 and the optimal value of the objective function, L for problem 2 (a). 2 (c) For each feasible Extreme Point in Problem 2 (a), Complete the following table (add additional rows as needed): Point x1 x2 Optimal? (Y/N] Why? 0.0 0.0 0.0

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Problem 2 2 (a) Solve the following linear program graphically Identify the feasible region and the optimal solution. Plot the objective function as a double dashed line broken line (==3===) through the optimal point. Label the feasible extreme points starting with the feasible extreme point with coordinates closest to X1, X2] = [0, 0] as A, and continuing counter-clockwise for the other feasible extreme points. Minimize Z = 15 X1 15 X2 S. t. - 2X1 2 X1 2 X2 s 16 2 X2 s 16 X1 X2 315 X2 X1, X2 0 2 (b) Provide the optimal solution, X1, X2: and the optimal value of the objective function, Z. for problem 2 (a). 2 (c) For each feasible Extreme Point in Problem 2 (a), Complete the following table (add additional rows as needed): Point x1 Optimal? (YIN] x2 Why? 00 0.0 00
Transcribed Image Text:Problem 2 2 (a) Solve the following linear program graphically Identify the feasible region and the optimal solution. Plot the objective function as a double dashed line broken line (==3===) through the optimal point. Label the feasible extreme points starting with the feasible extreme point with coordinates closest to X1, X2] = [0, 0] as A, and continuing counter-clockwise for the other feasible extreme points. Minimize Z = 15 X1 15 X2 S. t. - 2X1 2 X1 2 X2 s 16 2 X2 s 16 X1 X2 315 X2 X1, X2 0 2 (b) Provide the optimal solution, X1, X2: and the optimal value of the objective function, Z. for problem 2 (a). 2 (c) For each feasible Extreme Point in Problem 2 (a), Complete the following table (add additional rows as needed): Point x1 Optimal? (YIN] x2 Why? 00 0.0 00
Expert Solution
Step 1

The given minimization problem is:

Minimize Z=15x1-15x2

Subject to:

-2x1+2x2≤16                     …12x1-2x2≤16                     …2x1+x2≤15                     …3x2≤9                       …4x1,x2≥0

(a).

Consider the equations:

-2x1+2x2=162x1-2x2=16x1+x2=15x2=9

Therefore the feasible region can be drawn as:

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