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 relevant characteristics of these meats:
|
Meat1 |
Meat 2 |
Meat 3 |
| Cost Per Pound |
.75 |
.87 |
.98 |
| %Fat |
.15 |
.10 |
.05 |
| %Protein |
.7 |
.75 |
.8 |
| %Water |
.12 |
.10 |
.08 |
| %Filler |
.03 |
.05 |
.07 |
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.
a. Formulate an MOLP for this problem.
b. Implement your formulation in a spreadsheet and individually optimize the two objectives under consideration.
c. How much profit must be forfeited to fill this order using the mix that minimizes the fat content?
d. Solve this problem with the objective of minimizing the maximum percentage deviation from the target values of the goals. What solution do you obtain?
e. Assume that the owner considers minimizing the fat content twice as important as maximizing profit. What solution does thisimply?