HWChapter4

# HWChapter4 - Name 4.1 Problem Set 101 MAXIMIZATION BY THE...

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Name:_________________________________ 4.1 Problem Set 101 MAXIMIZATION BY THE SIMPLEX METHOD Solve the following linear programming problems using the simplex method. 1) Maximize z = x 1 + 2x 2 + 3x 3 subject to x 1 + x 2 + x 3 12 2x 1 + x 2 + 3x 3 18 x 1 , x 2 , x 3 0 2) Maximize z = x 1 + 2x 2 + x 3 subject to x 1 + x 2 3 x 2 + x 3 4 x 1 + x 3 5 x 1 , x 2 , x 3 0 3) A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and \$20 of capital, and each acre of corn requires 16 hours of labor and \$40 of capital. The farmer has at most 800 hours of labor and \$2400 of capital available. If the profit from an acre of wheat is \$80 and from an acre of corn is \$100, how many acres of each crop should she plant to maximize her profit?

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102 4.1 Problem Set Name:_________________________________ 4) A factory manufactures chairs, tables and bookcases each requiring the use of three operations: Cutting, Assembly, and Finishing. The first operation can be used at most 600 hours; the second at most 500 hours; and the third at most 300 hours. A chair requires 1 hour of cutting, 1 hour of assembly, and 1 hour of finishing; a table needs 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; and a bookcase requires 3 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is \$20 per unit for a chair, \$30 for a table, and \$25 for a bookcase, how many units of each should be manufactured to maximize profit? 5).
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HWChapter4 - Name 4.1 Problem Set 101 MAXIMIZATION BY THE...

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