Linear Programming Model for Maximizing Profit of a Production Schedule

Ms. Olsen, a coffee processor, markets three blends of coffee. They are Brand X, Minim and Taster's Reject. Ms. Olsen uses two types of coffee beans, Columbian and Mexican, in her coffee. The following chart lists the compositions of the blends.

Blend Columbian Beans Mexican Beans
Brand X 80% 20%
Minim 50% 50%
Taster's Reject 30% 70%

Ms. Olsen HAS purchased 20,000 pounds of Columbian beans at 90 cents per pound, and she has purchased 30,000 pounds of Mexican beans at 50 cents per pound. The beans have been delivered and are within the warehouse ready to use for coffee production. Unused Columbian beans can be sold at cost to another processor, but unused Mexican beans can be sold only for 55 cents per pound. Due to warehouse space limitations, Ms. Olsen must dispose of all unused beans.

Brand X sells for $2.60 per pound, Minim sells for $2.50 per pound, and Taster's Reject brings $2.34 per pound. All three products have the same production and packaging costs of $1.60 per pound.

Ms. Olsen is interested in finding the production schedule that will maximize profit.

Formulate a relevant linear programming model for this problem and determine the solution that maximizes profit (sales -cost)