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1. For the following linear program, maximize 7x112x29x3 subject to x13x23x3 4, 2x13x22x3 ≤5, 2x14x2+3x3 ≤7, x1, x2, x30 determine whether x = (³, ½, ½) is an optimal solution using the principle of com- plementary slackness. 2. For the following linear program maximize x18x23x3 subject to 2x1 +8x2 + 2x3 ≤ 4, 2x14x23x3 <4, x12x2x3 ≤ 1, x1, x2, x30 determine whether x = (0, 1, 0) is an optimal solution using the principle of com- plementary slackness.

1. For the following linear program, maximize 7x112x29x3 subject to x13x23x3 4, 2x13x22x3 ≤5, 2x14x2+3x3 ≤7, x1, x2, x30 determine whether x = (³, ½, ½) is an optimal solution using the principle of com- plementary slackness. 2. For the following linear program maximize x18x23x3 subject to 2x1 +8x2 + 2x3 ≤ 4, 2x14x23x3 <4, x12x2x3 ≤ 1, x1, x2, x30 determine whether x = (0, 1, 0) is an optimal solution using the principle of com- plementary slackness.

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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1. For the following linear program, maximize 7x112x29x3 subject to x13x23x3 4, 2x13x22x3 ≤5, 2x14x2+3x3 ≤7, x1, x2, x30 determine whether x = (³, ½, ½) is an optimal solution using the principle of com- plementary slackness. 2. For the following linear program maximize x18x23x3 subject to 2x1 +8x2 + 2x3 ≤ 4, 2x14x23x3 <4, x12x2x3 ≤ 1, x1, x2, x30 determine whether x = (0, 1, 0) is an optimal solution using the principle of com- plementary slackness.
Transcribed Image Text:1. For the following linear program, maximize 7x112x29x3 subject to x13x23x3 4, 2x13x22x3 ≤5, 2x14x2+3x3 ≤7, x1, x2, x30 determine whether x = (³, ½, ½) is an optimal solution using the principle of com- plementary slackness. 2. For the following linear program maximize x18x23x3 subject to 2x1 +8x2 + 2x3 ≤ 4, 2x14x23x3 <4, x12x2x3 ≤ 1, x1, x2, x30 determine whether x = (0, 1, 0) is an optimal solution using the principle of com- plementary slackness.
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