Exercise 2-1

A large-scale distributor of dressed meats which specializes in servicing the hotel market has recently received an order from a large hotel chain for 10,000 pounds of ground meat loaf containing ground beef, port, and veal, and soybean paste. Based on flavor considerations, as well as nutritional needs, the order specifies that:

1. The ground beef comprise between 40% and 60%, by weight, of the mix.
2. The ground pork comprise between 20% and 30%
3. The ground veal comprise between 10% and 40%
4. The ground pork, by weight, comprise not more than one and one-half times the weight of the veal
5. The mix must be at least 30% protein an not more than 12% fat.

The table below gives the protein and fat composition, by weight, of the four ingredients.

An analysis based on prevailing stock-yard prices, percent usable meat (recognizing waste in the dressing process) and labor costs indicated that the cost per pound of the four ingredients is as shown in the table. Formulate a linear program to determine the optimal composition of the meat loaf.