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How much profit must be forfeited in order to fill this order using the mix that minimizes the fat content?

05 / 03 / 2018 Assignment

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The owner of the Weiner-Meyer meat-processing plant wants to determine the best
blend of meats to use in the next production run of hamburgers. Three sources of meat
can be used. The following table summarizes the relevant characteristics of these
meats:

Cost per Pound
% Fat
% Protein
% Water
% Filler

Meat 1
$0.75
15%
70%
12%
3%

Meat 2
$0.87
10%
75%
10%
5%

Meat 3
$0.98
5%
80%
8%
7%

A local elementary school has ordered 500 pounds of meat for $1.10 per pound. The
only requirement is that the meat consist of at least 75% protein and at most 10% each
of water and filler. Ordinarily, the owner would produce the blend of meats that achieved
this objective in the least costly manner. However, with the concern of too much fat in
school lunches, the owner also wants to produce a blend that minimizes the fat content
of the meat produced.

*Formulate an Multiple Objective Linear Programming model for this problem.
* Implement your formulation in a spreadsheet, and individually optimize the two
objectives under consideration.
* How much profit must be forfeited in order to fill this order using the mix that minimizes
the fat content?

* Solve this problem with the objective of minimizing the maximum percentage deviation
from the target values of the goals. What solution do you obtain?
* Assume the owner considers minimizing the fat content twice as important as
maximizing profit. What solution does this imply?

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