A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant

Question

A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, and both of them are used to make the rubber strips. Machine-1 is available 180 hours per month and Machine-2 is available 200 hours per month. Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. For processing one strip of Polyisoprene, it takes 3.5 hours on Machine-1 and 4 hours on Machine-2.

a. Formulate an all-integer model that will determine how many units of each type of the rubber should be used to maximize the manufacturer’s contribution to profit if he gets a profit of $20 on Butadiene and $26 on Polyisoprene?

b. Use Excel Solver to determine the optimal number of units produced of each type of rubber (Butadiene and Polyisoprene).

Explanation / Answer

Total Machine 1 hours = 180 per month

Total Machine 2 hours = 200 per month

a.) Let the number of units of butadiene that showed be made is x, and Polyisoprene is y.

Objective function:

Max 20 x + 26 y

Subject to:

2.75 x + 3.5 y 180

3 x + 4 y 200

x 0, y 0

b.) x = 40 , y = 20

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