Consider a profit maximizing product mix problem that has three products (X1, X2

Question

Consider a profit maximizing product mix problem that has three products (X1, X2, and X3). One of the many constraints on production is the inventory of plastic pellets. The expression for this constraint is shown below. All units are in grams.

Plastic Pellets: 12X1 + 5X2 + 4X3 <= 200,000

After running the entire linear program, the solution is X1 = 10,000, X2 = 5000, and X3 = 4000

1. What is the total amount of pellets available before production?

2. What is the total amount of pellets left after production?

3. Based on your calculations, is the constraint binding?

4. If you added 20 more grams of plastic pellets to inventory, would you expect the objective value to increase, decrease or stay the same? Why or why not?

Explanation / Answer

Qn 1:

From the Equation , we can derive that the number of pellets must be a maximum of 200,000 since the total pellets used cannot be more than the number of pellets available.

Qn 2:

12*X1 + 5*X2 + 4*X3 = 12*10,000 + 5*5,000 + 4*4,000

= 120,000 + 25,000 + 16,000

= 161,000

Qn. 3.

Based on the calculations , 161,000 pellets were used which is less than the total available pellets of 200,000

Hence, the constraint is binding

Qn. 4,

By definition of objective value, the value of an object, good or service, is intrinsic or contained in the item itself. The same number of pellets are being used for each product and hence their objective values will not change.

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