Resource allocation and optimal product mix at a fish and seafood processing company

A company which processes lobster, smelt and shrimp is discussed. The company's main product is lobster. This product can be transformed at a rate of 45,000 to 50,000 pounds in a period of 8 hours. The company employs approximately 250 employees during peak season and has annual sales of approximately $10 million, with 95% of its products being exported to foreign countries. With the continually increasing international competition, the pressures to comply to stricter international standards and the decreasing annual volume of lobster catches, the company wanted to know the optimal product mix that maximizes profits within a set of limited resources and limited available time. The product mix consists of 12 lobster products. These product contain different parts of lobster meat with pre-specified percentages. The pre-specified percentages are defined by the specifications of each product. A linear programming model is formulated to find the optimal product mix.