Problems Linear Programming Models
 Linear Programming Models - Product Mix for A, B and C

A company makes three products in three processes as shown in the schematic below. The products are A, B and C. The products are made with the raw materials 1, 2 and 3. Processes B and C also require the outputs of the previous processes as input. Each unit processed in B requires two units of product A, and each unit of product C requires 1.2 units of product B. Additional information about the products and raw materials is shown in the tables. The product revenues are for units sold, not for units used in other processes.

 Product A B C Raw Mat. 1 2 3 Unit Rev. \$100 \$350 \$500 Unit Cost \$50 \$20 \$40 Max Sales 100 150 200 Available 200 150 200

Each unit processed in A requires 1 unit of RM 1.

Each unit processed in B requires 2 units of Product A, 1 additional unit of RM 1 and 0.6 units of RM 2.

Each unit processed in C requires 1.2 units of Product B, 0.3 additional units of RM 1, 0.2 additional units of RM 2 and 1 unit of RM 3.

Write and solve the linear programming model that finds the optimum amount of each product to produce and the amounts of raw materials used. The goal is to maximize profit.

Operations Research Models and Methods
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by Paul A. Jensen