A manufactures produces two types of soap bars using two machines, A and B. A is operated for 2 minutes and B for 3 minutes to manufacture the first type, while it takes 3 minutes on machine A and 5 minutes on machine B to manufacture the second type. Each machine can be operated at the most for 8 hours per day. The two types of soap bars are sold at a profit of ₹0.25 and ₹0.50 each. Assuming that the manufacture can sell all the soap bars he can manufacture, how many bars of soap of each type should be manufactured per day so as to maximize his profit?

Let x and y be number of soaps be manufactured of 1^st and 2^nd type.

∴According to the question,

2x + 3y 480 , 3x + 5y 480, x , y

Maximize Z = 0.25x + 0.50y

The feasible region determined by 2x + 3y 480 , 3x + 5y 480, x , y is given by

The corner points of feasible region are A(0,96) , B(0,0) , C(160,0).

The value of Z at corner points are

The maximum value of Z is 48 at point (0,96).

Hence, the manufacturer should make 96 soaps of the 2^nd type to make maximum profit.