1. Give the dual of each of the following linear programs:(a)maximize 5x₁ + 8x₂ + x3 + 2x₁subject to(b)minimizesubject to3x₁ + 3x₂ + 7x3 + 8x ≤ 15,2x28x3-7x4 ≥ 10,9x16x22x3+4x4 = 5,I1, I2, I3 ≥ 0,4 unrestricted3x₁ + 7x3 +9x4-₁ + 3x₂ - 32x1 + 5x₂ + 8x3 + 9x₁ ≥ 1,-10₁ ≤ -12,x₁ + 4x2 + 8x32 -4,I1, I2 ≥ 0,X3 ≤ 0,I 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: 1. Give the dual of each of the…

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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An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $ . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $ per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…
Consider the following linear program: maximize subject to Show Transcribed Text 3x1 + x2 + 4x3 1+3x2 + x3 ≤ 5 1 + 2x2 + 2x3 ≤7 21, 22, 23 20 (a). What is the corresponding dual problem? (b). Solve the dual problem graphically. (c). Use complementarity conditions for the primal-dual pair to solve the primal problem. If solving problems need MATLAB or Python, plz show me the Code that would help me a lot!!
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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1a and 2a please written out
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