Question

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine and 3hours of craftman’s time in its making, while a cricket bat takes 3 hours of machine time and 1 hour of craftman’s time. In a day, the factory has availability of not more than 42 hours of machine time and 24 hours of craftman’s time.

1. What no. of rackets and bats must be produced if the factory is to work at full capacity?
2. If the profit on a racket and a bat is 10 find maximum profit.

Answer 1

Let the number of rackets made = x and that of bats = y.

Maximise; Z = x + y

Machine constraints 1.5x + 3y ≤ 42

Craftsman’s constraint 3x + y ≤ 24

Therefore; Maximise; Z = x + y

x + 2y ≤ 14, 3x + y ≤ 24, x ≥ 0, y ≥ 0

In the figure the shaded region OABC is the fesible region. Here the region is bounded. The

corner points are O(0, 0), A(8, 0), B(4, 10), C(0, 14).

Given; Z = x + y

Corner points	Value of Z
O	Z = 0
A	Z = 8 + 0 = 8
B	Z = 4 + 12 = 16
C	Z = 0 + 14 = 14

Since maximum value of Z occurs at B, the solution is Z = 16, (4, 12).