Find the optimal solution of the Linear Programmingproblem below using Big M method. Write the standardform first and then present your solution. Indicate if thereare any special cases.Maximize Z = 2x1 + 3x2 - X3 - 3x4Subject to2x1 + 3x2 - X3 - 5x4 2 25X1- X2 + 7x3 + X4 2 14-X1 + 2x2+ 3x4 2 -6X4= 3X1, X2, X3, X4 2 0

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Answered: Find the optimal solution of the Linear…

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…
Is this constraint linear or able to be included as a constraint in a linear programming problem? 4X1 – (1/3)X2 = 75
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Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Use the simplex method to solve the linear programming problem. z= 5x, +2x2 +X3 4x1 +4x2 + Maximize subject to X3 S36 X1 + 3x2 + 5x3 511 X1 20, X2 20, x3 20. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. when x, X2 =, x3 = The maximum is and S2 %3D O A. B. There is no maximum.
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Q3/ Solve by simplex method the following linear programming problem: (3 tables) Max Z = 3x₁ + 5x₂ + 4x3 Sub.to 2x₂ + 3x₂ ≤8 2x2 + 5x3 ≤ 10 3x + 2x2 + 4x3 ≤ 15 X1, X2, X3 20

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