Explanation Given: Every church group requires 2 hours of writing letters and 1 hour of follow-ups for Dona to raise money. Each labor union needs 2 hours of writing letters and 3 hours of follow-ups for Donna to raise money. Donna has 16 hours to write letters and 12 hours to follow up every month and she can raise $100 and $200 from a church and a labor union respectively. Explanation: Let the number of church groups and the labor unions Donna contacts be denoted by x and y respectively. Let the total money raised be denoted by p dollars. p = 100 x + 200 y The restrictions she has can be represented by the following set of inequalities, 2 x + 2 y ≤ 16 x + 3 y ≤ 12 Also, the number of units produced can’t be negative. This gives rise to two non-negative constraints. x ≥ 0 , y ≥ 0 This optimization problem can be written as: Maximize p = 100 x + 200 y Subject to, 2 x + 2 y ≤ 16 x + 3 y ≤ 12 With x ≥ 0 , y ≥ 0 The problem can be solved using MS-Excel. Proceed with the following steps. Step 1: Open an empty workbook and type the initial guesses for variables x and y as 0 and 0 respectively in cells A2 and B2. Step 2: In cell C2, type in the objective function as the formula replacing x with A2 and y with B2. Step 3: Now, add the left side of the constraints as formulas in cells C3, C4, C5 and C6. Use A2 for x and B2 for y .

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 4.2, Problem 33E

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The highest and lowest values of amounts on raised from church groups and a labor union that do not change the solution for the system.

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Chapter 4.2, Problem 32E

Chapter 4.2, Problem 34E

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Chapter 4 Solutions

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The highest and lowest values of amounts on raised from church groups and a labor union that do not change the solution for the system.

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The highest and lowest values of amounts on raised from church groups and a labor union that do not change the solution for the system.

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