Problem 4 Consider the following linear program: min 6x1 +4x2+2x3 s.t. x₁+x₂x3 ≥ −1 2x1 + 2x3 ≥ 1 Xi ≥ 0 (a) Write the dual linear program and solve graphically. Your graph should include: labels for each constraint, light shading of the feasible region, labels for each basic feasible solution, and the objective value for each basic feasible solution. (b) Use complementary slackness to find the corresponding optimal solution to the primal problem.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 4
Consider the following linear program:
min 6x1 +4x2+2x3
s.t.
X3 ≥ −1
X1 + X₂
2x1 + 2x3 ≥ 1
Xį ≥ 0
(a) Write the dual linear program and solve graphically. Your graph should include: labels for each
constraint, light shading of the feasible region, labels for each basic feasible solution, and the objective
value for each basic feasible solution.
(b) Use complementary slackness to find the corresponding optimal solution to the primal problem.
Transcribed Image Text:Problem 4 Consider the following linear program: min 6x1 +4x2+2x3 s.t. X3 ≥ −1 X1 + X₂ 2x1 + 2x3 ≥ 1 Xį ≥ 0 (a) Write the dual linear program and solve graphically. Your graph should include: labels for each constraint, light shading of the feasible region, labels for each basic feasible solution, and the objective value for each basic feasible solution. (b) Use complementary slackness to find the corresponding optimal solution to the primal problem.
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