Question

You manufacture two products, A and B, each of which you sell for $1 profit. Product A requires 5 blobs and 3 globs, and product B requires 3 blobs and 5 globs. Your supplier has 120 blobs and 120 globs available.

Use the Excel Solver (or graphical analysis) to answer the following questions.

9. If the profit on B increases to $2, can you increase profit by trading 30 blobs for 30 globs?

10. As the profit on B changes from $1 to $1.66, does your business decision concerning product mix stay the same?

11. As the profit on B changes from $1.66 to $1.67, does your business decision concerning product mix change?

12. If the profit for A and B increase to $2 each, will you want to trade excess blobs for globs?

Answer 1

Decision Variables:

Number of product A = A

Number of product B = B

Objective Function:

Here the objective is to maximize the profit. Each product gives profit of $1.

Objective function is:

MAX A + B

Constraints:

We cant use blobs and globs more than the available quantity

5*A + 3*B <= 120

3*A + 5*B <= 120

The number of products cant be in negative.

A, B >= 0

Putting the Equations in Excel:

Variable Parameters:

Optimal Solution:

Sensitivity Analysis:

Question – 9:

As both constraint has same shadow price, the increment of 30 in one and decrement of 30 in another wont change the profit. The current solution also will be optimal. Hence if we increase the profit of B to $2, the profit will increase.

Question – 10:

There wont be any change as the current solution is optimal till a profit of $1.67

Question – 11:

Yes. The optimality changes at a profit of $1.667 (which comes in between 1.66 and 1.67). Hence the decision will change

Question – 12:

No. This is because both the products yields same profit and there wont be any change in profit.

********

IF YOU HAVE ANY DOUBT, KINDLY COMMENT. I WOULD LOVE TO HELP YOU!!!

IF YOU LIKE THE ANSWER, PLEASE GIVE AN UP-VOTE OR THUMB UP. THIS WILL ENCOURAGE ME TO ANSWER MORE!!