1. Give the dual of each of the following linear programs:maximize 5x1 + 8x2 + x3 + 2x4subject to(b)minimizesubject to3x1 + 3x2 + 7x3 + 8x4 ≤ 15,2x28x3-7x4 ≥ 10,9x16x22x3+4x4 = 5,X1, X2, X3 ≥ 0,4 unrestricted3x1 + 7x3 + 9x4-x1 + 3x2x3 - 10x4≤-12,2x1 +5x2 + 8x3 +9x4 ≥ 1,x1 +4x2+8x3 -x4,X1, X2 ≥ 0,X3 ≤ 0,4 unrestrictedHint: Remember to first rewrite all the constraints and variables into thecorrect forms for minimisation!

Solution:Primal is MAX Zx = 5 x1 + 8 x2 + x3 + 2 x4 subject to 3 x1 + 3 x2…

Answered: 3 (b) maximize 5x1 +8x2 + x3 + 2x4…

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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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,