Question

A company manufactures two types of sweaters : type A and type B. It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater. The company can make at most 300 sweaters and spend at most Rs 72000 a day. The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100. The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.
Formulate this problem as a LPP to maximise the profit to the company.

Answer 1

Let x and y be the number of sweaters of type A and type B respectively.

From the given information, we have the following constraints.

360x + 120y ≤ 72000 ⇒ 3x + y ≤ 600  ......(i)

x + y ≤ 300 ......(ii)

x + 100 ≥ y ⇒ y ≤ x + 100  ......(iii)

Profit (Z) = 200x + 120y

Hence, the required LPP to maximise the profit is

Maximise Z = 200x + 120y subject to the constraints

3x + y ≤ 600, x + y ≤ 300, y ≤ x + 100, x ≥ 0, y ≥ 0.