Question

Assume we have two products X and Y . To make a X requires 1/2 hour of cutting and 20 minutes of stitching. To make a Y requires 15 minutes of cutting and 1/2 hour of stitching. The profit on a X is 40 and on a pair of Y 50. The business operates for a maximum of 8 hours per day. Determine how many X and Y should be made to maximize profit and what the maximum profit is.

Answer 1

Cutting time : 1/2 x + 15/60 y 8  

2 x + y 32

When x=0 , y=32

And y =0, x=16

Stitching time : 20/60 x+ 1/2 y 8

2x +3y 48

When x=0, y=16

When y=0 , x=24

By plotting these inequalities, we get the graph as shown below:

Objective function: Profit function = 40x +50y

From the graph we can see the feasible points (0,16), (16,0) and (12,8).

(i) At (0,16) : P= 40(0) +50(16) = 800

(ii) At (16,0) : P= 40(16) + 50(0)= 640

(iii) At (12,8):P =40(12) + 50(8)= 480+ 400= 880

The maximum profit is 880 for X=12 and Y=8 .