A manufactures pr

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.