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3 (b) maximize 5x1 +8x2 + x3 + 2x4 subject to minimize subject to 3x1 + 3x2 + 7x3 + 8x4≤ 15, 2x28x3-7x4 ≥ 10, 9x16x22x3+4x4 = 5, X1, X2, X3 ≥ 0, 4 unrestricted 3x1 + 7x3 +9x4 -x1 + 3x2-x3-10x4≤-12, 2x1 +5x2 + 8x3+9x4 ≥ 1, x1 +4x2+8x3 -x4,

3 (b) maximize 5x1 +8x2 + x3 + 2x4 subject to minimize subject to 3x1 + 3x2 + 7x3 + 8x4≤ 15, 2x28x3-7x4 ≥ 10, 9x16x22x3+4x4 = 5, X1, X2, X3 ≥ 0, 4 unrestricted 3x1 + 7x3 +9x4 -x1 + 3x2-x3-10x4≤-12, 2x1 +5x2 + 8x3+9x4 ≥ 1, x1 +4x2+8x3 -x4,

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. Give the dual of each of the following linear programs: maximize 5x1 + 8x2 + x3 + 2x4 subject to (b) minimize subject to 3x1 + 3x2 + 7x3 + 8x4 ≤ 15, 2x28x3-7x4 ≥ 10, 9x16x22x3+4x4 = 5, X1, X2, X3 ≥ 0, 4 unrestricted 3x1 + 7x3 + 9x4 -x1 + 3x2x3 - 10x4≤-12, 2x1 +5x2 + 8x3 +9x4 ≥ 1, x1 +4x2+8x3 -x4, X1, X2 ≥ 0, X3 ≤ 0, 4 unrestricted Hint: Remember to first rewrite all the constraints and variables into the correct forms for minimisation!
Transcribed Image Text:1. Give the dual of each of the following linear programs: maximize 5x1 + 8x2 + x3 + 2x4 subject to (b) minimize subject to 3x1 + 3x2 + 7x3 + 8x4 ≤ 15, 2x28x3-7x4 ≥ 10, 9x16x22x3+4x4 = 5, X1, X2, X3 ≥ 0, 4 unrestricted 3x1 + 7x3 + 9x4 -x1 + 3x2x3 - 10x4≤-12, 2x1 +5x2 + 8x3 +9x4 ≥ 1, x1 +4x2+8x3 -x4, X1, X2 ≥ 0, X3 ≤ 0, 4 unrestricted Hint: Remember to first rewrite all the constraints and variables into the correct forms for minimisation!
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