Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 3.9, Problem 7P

Explanation of Solution

Formulation of linear problem

  • The steps for defining a linear problem include:
    • Identifying the decision variables.
    • Writing the objective function.
    • Mentioning the constraints.
    • Explicitly stating the non-negativity restriction.
  • A problem will be a linear problem if and only if the decision variables, objective function and constraints all are linear functions.
  • If all the three conditions are satisfied, then it is a linear problem.
  • Let C2 be the pounds of cream cheese produced, P2 be the pounds of cottage cheese produced, HF be the pounds of high fat milk purchased, LF be the pounds of low fat milk purchased, HFE be the pounds of high fat milk put through evaporator, LFE be the pounds of low fat milk put through evaporator, HF1 be the pounds of high fat milk used to make cream cheese, LF1 be the pounds of low fat milk used to make cream cheese, C1 be the cream input to make cream cheese, HF2 be the pounds of high fat milk used to make cottage cheese, LF2 be the pounds of low fat milk used to make cottage cheese and C2 be the cream input to make cottage cheese.
  • Then the changed formulation is:

    Max z = 1.1P1 + .8P2 -.4HFE - .4LFE -.4LF - .8HF

    Subject to

    P1>=1000, P2>=1000, P1<=1500, P2<=2000P1 = HF1 + LF1 +C1P2 = 

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Chapter 3 Solutions

Introduction to mathematical programming

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