1. A chemical company produces two types of solvents. One solvent (Varsol) takes

Question

1. A chemical company produces two types of solvents. One solvent (Varsol) takes three hours to go through the cracking process and two hours to go through the refining process. The other solvent (Moonshine) takes two hours to go through cracking, and four hours through refining. The cracking tower has sixty hours of availability, and the refining tower has eighty hours of availability Set up the formula and solve using the equation method. What is the optimal combination from a production efficiency standard? (20 Points)

Explanation / Answer

Let V: Amount of Varson produced
     M : Amount of Moonshine produced
     C : Time for which cracking tower is in use
     R : Time for which refining tower is in use

The objective is to choose a combination for optimal production efficiency. In other words, the objective is to maximize the total production of both the solvents combined with availability of cracking tower and refining tower as the constraints.

Objective Function: Z(max): V + M
Constraints:
C = 3V + 2M (Varsol leeds 3 hours of cracking and Moonshine needs 2 hours of cracking)
R = 2V + 4M (Varsol leeds 2 hours of refining and Moonshine needs 4 hours of refining)
C <= 60 (Cracking tower has only 60 hours of availability)
R <= 80 (Refining tower has only 80 hours of availability)

Now when we solve the objective function with respects to the constraints we get,

V = 10 and M = 15 (We can solve the above inequalities using Excel Solver)

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