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.

17. Can you obtain more blobs and globs for product B by producing negative quantities of product A?

Answer 1

Let us assume the following:

Number of units of Product A = X1

Number of units of Product B = X2

The objective function is profit maximization:

Maximise Z = 1X1 + 1X2

Constraint 1: 120 blobs available:

5X1 + 3X2 <= 120

Constraint 2: 120 globs available:

3X1 + 5X2 <= 120

Solving the problem graphically:

The two constraints have to be plotted on a graph.

The feasible region has been highlighted. The objective function value has to be calculated at the 4 corner points (A, B, C, O).

A (0, 24) : Z = ( 1 x 0) + ( 1 x 24) = 0 + 24 = 24

B ( 15, 15) : Z = ( 1 x 15) + ( 1 x 15) = 15 + 15 = 30

C ( 24, 0): Z = ( 1 x 24) + ( 1 x 0) = 24 + 0 = 24

O (0, 0) : Z = ( 1 x 0) + ( 1 x 0) = 0 + 0 = 0

The objective function value is maximum at B ( 15, 15).

Therefore, the optimal solution is as follows:

Number of units of Product A = X1 = 15

Number of units of Product B = X2 = 15

Maximum Profit = Z = $ 30

The above solution is the most optimal solution. It will result in the highest profit along with the best utilization of blobs and globs. If the quantity of Product A is reduced from this solution, the resulting solution shall not be optimal.

Further, negative quantities of A cannot be produced, The minimum quantity of A can be 0.

Therefore, more number of blobs and globs for product B cannot be obtained by producing product A in negative quantities.