Sensitivity Analysis

Question

In an Operations Research Problem:

"A beverage company wants to produce a new juice with a mixed flavor, using only orange and pineapple flavors. Orange flavor contains 5% of vitamin A and 2% of vitamin C. Pineapple flavor contains 8% of Vitamin C. The company's quality policies indicate that at least 20L of orange flavor should be added to the new juice and vitamin C content should not be greater than 5%. Determine the optimum amount of each flavor that should be used to satisfy a minimum demand of 100L of juice."

The linear programming model is as follows:

Let X1: Amount in L of orange flavor Let x2: Amount in L of pineapple flavor

min Z=1000x1+400x2

0.02x1+0.08x2<=0.05(x1+x2)

x1>=20

x1+x2>=100

That gives x1=50 L and x2=50L of orange and pineapple flavors.

However, the company wants to know what would happen if the vitamin C requirement is to be not greater than 7%?

In this case, as the change in the coefficient of (x1+x2) in the first restriction would imply more than 1 change at a time, the model would have to be run again to determine the impact on the optimal solutions?.

But also, S.A. only applies when the value of the right hand side of the restrictions is changed, so would S.A. apply here?

Thanks.

Answer 1

If you are minimizing cost, then there is no advantage to producing more than the required 100 liters of juice. Using that, you can rewrite the model so that the 5% limit on vitamin C is part of a constant right-hand side, allowing you to apply sensitivity analysis.