Product Mix Problem Statement

Ray's Red Hots, Inc. manufactures five types of sausages. The number of pounds of four ingredients—veal, pork, beef, and casing—used per unit of product and the profit generated per unit are given in the table below.

Table 5. Ray’s Red Hots data summary

Products	Veal	Pork	Beef	Casing	Profit Per Unit
Summer Sausage	0.00	2.50	1.00	1.00	$1.25
Bratwurst	4.00	1.00	0.00	1.50	$1.80
Italian Sausage	1.00	3.00	1.50	1.00	$1.40
Pepperoni	0.00	4.00	0.00	2.00	$2.10
Polish Sausage	0.00	1.00	3.00	1.50	$1.70

Limited amounts of ingredients are available for the next production cycle. Specifically, only 12,520 pounds of veal, 14,100 pounds of pork, 6,480 pounds of beef, and 10,800 pounds of casing are available.

Complicating this situation is:

The unit profits are only estimates because all customer contracts have not been finalized.
The amount of casing used per unit might be more than anticipated because of production losses due to tearing or partial rejections during inspection.

The problem is to determine how many pounds of each product to produce in order to maximize gross profit without running out of meat ingredients or casing during the manufacturing run.