Problems Linear Programming Models
 Linear Programming Models - Product Mix with Goals

Three products can be produced at two machining centers. The products may be produced in fractional amounts. The linear relationships describing this situation are listed below. The variables are:

A, B and C are the amounts of the three products in units.

R1 and R2 are the amounts of raw materials used in kilograms.

T1 and T2 are the times used in the two machining centers.

 Profit: P = 20A + 30B + 25C - 6R1 - 8R2 Time required on machine 1: T1 = 5A + 8B + 10C (hours) Time required on machine 2: T2 = 8A + 6B + 2C (hours) Raw material 1 used: R1 = 1A + 2B + 0.75C Raw material 2 used: R2 = 0.5A + 1B + 0.5C Market Limits:

We have three goals listed in order of priority below. These are not strict limits, but only goals.

Goal 1: The minimum production of the three products is to be equal to at least 5 units.

Goal 2: The profit should be at least 150.

Goal 3: The total time used on the two machines should be no more than 150 hours.

Write the complete linear programming model that will solve this goal programming problem. Include the strict constraints that each machine can operate no more than 100 hours individually. Solve the problem to find the optimum production quantities.

Operations Research Models and Methods
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by Paul A. Jensen