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Consider the following LP: max z = 21 – 4x2 s.t. x1 - x2 <1 X1, X2 > 0. (a) Write down the dual of this LP. What is the dual optimal solution? (b) Use the complementary slackness property and the dual optimal solution to find the optimal solution to the original (primal) LP. (Please do not solve it directly using the graphical method or the simplex method.) (c) Let c be the objective coefficient of x1, and suppose that c1 can actually take any value (c is currently 2). Discuss how the optimal objective value changes as c1 takes different values.

Consider the following LP: max z = 21 – 4x2 s.t. x1 - x2 <1 X1, X2 > 0. (a) Write down the dual of this LP. What is the dual optimal solution? (b) Use the complementary slackness property and the dual optimal solution to find the optimal solution to the original (primal) LP. (Please do not solve it directly using the graphical method or the simplex method.) (c) Let c be the objective coefficient of x1, and suppose that c1 can actually take any value (c is currently 2). Discuss how the optimal objective value changes as c1 takes different values.

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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Consider the following LP: max z = 2.x1 – 4x2 s.t. x1 – x2 <1 X1, X2 > 0. (a) Write down the dual of this LP. What is the dual optimal solution? (b) Use the complementary slackness property and the dual optimal solution to find the optimal solution to the original (primal) LP. (Please do not solve it directly using the graphical method or the simplex method.) (c) Let c be the objective coefficient of x1, and suppose that c can actually take any value (c is currently 2). Discuss how the optimal objective value changes as c1 takes different values.
Transcribed Image Text:Consider the following LP: max z = 2.x1 – 4x2 s.t. x1 – x2 <1 X1, X2 > 0. (a) Write down the dual of this LP. What is the dual optimal solution? (b) Use the complementary slackness property and the dual optimal solution to find the optimal solution to the original (primal) LP. (Please do not solve it directly using the graphical method or the simplex method.) (c) Let c be the objective coefficient of x1, and suppose that c can actually take any value (c is currently 2). Discuss how the optimal objective value changes as c1 takes different values.
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