Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
Expert Solution & Answer
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Chapter 3.9, Problem 2P

Explanation of Solution

Given:

Let x1 be the number of finished tables, xb be the number of unfinished tables.

Let y1 be the number of finished chairs, y2 be the number of unfinished chairs.

Objective function:

Profit=Revenue-Cost=[(revenue of finished table)(cost/ft of finished table)+(revenue of unfinished table)(cost/ft of unfinished table)+(revenue of finished chair)(cost/ft of finished chair)+(revenue of unfinished chair)(cost/ft of unfinished chair)]

  =(14040)x1+(7040)x2+(11030)y1+(6030)y2=100x1+30x2+80y1+30y2

Maximize z=100x1+30x2+80y1+30y2

Considering the constraints,

Constraint 1 and 2: At most, 4000 woods are available for purchase.

Constraint 3: At most, 6000 hours of labor are available to manufacture

Expressing the constraint 1 in terms of variables:

[(40 ft of wood required to manufacture table)+(30 ft of wood required to manufacture table)]4000040(x1+x2)+30(y1+y2)40000

Expressing

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Chapter 3 Solutions

Introduction to mathematical programming

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