A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (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 type B should be manufactured in a day to get maximum profit.

262.5

Let x and y toys of type A and B respectively be manufactured in a day.

The given problem can be formulated as follows:

Maximise $z=7.5x+5y$......(1)

subject to the constraints

$2x+y≤60$........(2)

$x≤20$........(3)

$2x+3y≤120$.........(4)

$x,y≥0$..........(5)

The feasible region determined by the constraints is as shown

The corner points of the feasible 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.

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.