For each of the following problems, perform these steps:• Write the dual problem for the problem as written.• Rewrite the problem in standard form.• Write the dual of the problem in standard form.• Explain why the two dual formulations are equivalent.Maximize z = 2x, + x2 + 3x3 + 4x4subject to4x1 + 2x2 + 5x3 + 5x4 < 104x1 + 2x2 + 5x3 + 5x4 2 53x, + 5x2 + 4x3 + x4 2 83x, + 5x, + 4x3 + x4s 15X1 + X2 + x3 + X4 = 20x1 2 0, x2 2 0, x3 2 0, x4 0.

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Answered: For each of the following problems,…

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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Use the method of linear programming to solve the problem.Compucraft sells personal computers and printers made by Peach Computers. The computers come in 12-cubic-foot boxes, and the printers come in 8-cubic-foot boxes. Compucraft's owner estimates that at least 30 computers can be sold each month and that the number of computers sold will be at least 50% more than the number of printers. The computers cost Compucraft $1,000 each and can be sold at a $1,000 profit, while the printers cost $300 each and can be sold for a $475 profit. Compucraft has 1,000 cubic feet of storage available for the Peach personal computers and printers and sufficient financing to spend $70,000 each month on computers and printers. How many computers and printers should Compucraft order from Peach each month to maximize profit? (Round your answers down to the nearest whole number.) computers printers What is that maximum profit?$
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