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maximize z(x1, x2) = x1+ 2x2 subject to = (x1, x2) E X. a) Use the graphical method to find an optimal solution x* and the optimal objective value z* z(x*) to this LP. b) What is the value of the level curve of the objective function passing through the optimal solution?

maximize z(x1, x2) = x1+ 2x2 subject to = (x1, x2) E X. a) Use the graphical method to find an optimal solution x* and the optimal objective value z* z(x*) to this LP. b) What is the value of the level curve of the objective function passing through the optimal solution?

Advanced Engineering Mathematics
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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Hello! I need help with the second part of this question, "given the feasible set you graphed in question 1, consider the following LP". Thank you!

Consider the set X e R? defined by the system of inequalities X = {R² : -x + x2 < 2, x1 + x2 < 5, 2x1 + x2 < 4, x1 > 0, x2 > 0}. (a) In the two-dimensional coordinate system (x1, x2), clearly draw the set X. You may use the attached graph paper. (b) List all extreme points and their coordinates. Given the feasible set X that you graphed in problem 1, consider the following linear program (LP): maximize z(x1, X2) = x1 + 2x2 subject to = (x1, x2) E X. (a) Use the graphical method to find an optimal solution x* and the optimal objective value z* = z(x*) to this LP. (b) What is the value of the level curve of the objective function passing through the optimal solution?
Transcribed Image Text:Consider the set X e R? defined by the system of inequalities X = {R² : -x + x2 < 2, x1 + x2 < 5, 2x1 + x2 < 4, x1 > 0, x2 > 0}. (a) In the two-dimensional coordinate system (x1, x2), clearly draw the set X. You may use the attached graph paper. (b) List all extreme points and their coordinates. Given the feasible set X that you graphed in problem 1, consider the following linear program (LP): maximize z(x1, X2) = x1 + 2x2 subject to = (x1, x2) E X. (a) Use the graphical method to find an optimal solution x* and the optimal objective value z* = z(x*) to this LP. (b) What is the value of the level curve of the objective function passing through the optimal solution?
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