1. Give the dual of each of the following linear programs:(a)maximize 100x₁ + 200x2 + 300x3 + 400x4subject tox1+2x2+3x3 - 4x ≤ 10,-5x16x27x3+8x4-20,9x1+102+11x3-12x4 = 30,X1, X30,x40,x2 unrestricted

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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!
Please can you help me with this linear programming question, I've tried seek an anser/guidance from chatgpt but it seems to get it wrong.
Is this constraint linear or able to be included as a constraint in a linear programming problem? 4X1 – (1/3)X2 = 75
2. Rewrite the following linear program in standard form.
2. Rewrite the following linear program in standard form. (1) s.t. min z = -5x1 - 6x2 - 7x3 -x1 - 5x2 3x3 ≥ 15 -5x1 - 6x2 + 10x3 ≤ 20 x1x2x3 = -5 x1 ≤ 0, x2 > 0, x3 unconstrained -
Convert the following linear program to standard form: Maximize z = 3x₁ + 5x2 - 4x3 ubject to 7x1 - 2x2 - 3x3 ≥4 - 2x1 + 4x2 + 8x3 = -3 5x13x2 - 2x3 ≤9 x1 ≥ 1, X₂ ≤7, X3 ≥ 0.
solve the following linear programming problem

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1. Give the dual of each of the following linear programs: (a) maximize 100x₁+2002+300x3 + 400x4 subject to x+2x2+3x3 - 4x4 ≤10, -5x-6x2-7x3+8x4-20, 9x1 +102+11x3 - 12x4 = 30, 11, 130, 14 ≤0, 12 unrestricted