#### Question

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

What number of rackets and bats must be made if the factory is to work at full capacity?

#### Solution

Let the number of rackets and the number of bats to be made be *x* and *y* respectively.

The machine time is not available for more than 42 hours.

:.1.5x+3y<=42

The craftsman’s time is not available for more than 24 hours.

:.3x+y<=24

The factory is to work at full capacity. Therefore,

1.5*x* + 3*y* = 42

3*x* + *y* = 24

On solving these equations, we obtain

*x* = 4 and *y* = 12

Thus, 4 rackets and 12 bats must be made.