A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the tune (in minutes) required for each toy on the machines is given below: Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. show that 15 toys of type A and 30 of the B should be manufactured m a day to get maximum profit.

Explanation

Let x and y toys of type A and B severally be factory-made in an exceedingly day.

The given drawback may be developed as follows:

Maximise` z=7.5x+5y`
subject to the constraints

`2x+y≤60`
`x≤20`
`2x+3y≤120`
`x,y≥0`
The possible region determined by the constraints is as shown

The corner points of the possible region are `A(20,0),B(20,20),C(15,30) and D(0,40)`
The value of z at these corner points are as follows.
so,The maximum value of z is `262.5` at `(15,30)`

Thus, the manufacturer should manufacture 15 toys of type A and 30 toys of type B to maximize the profit.