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 the company manufactures x number of type A sweaters and y number of type B.

The company spend at most Rs 72000 a day.

∴ 360x + 120y ≤ 72000

=> 3x+y≤ 600 …(i)

Also, company can make at most 300 sweaters.

∴ x+y≤ 300 …(ii)

Also, the number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100 i.e., y-x≤ 100

The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B

So, the objective function for maximum profit is Z = 200x + 120y subject to constraints. 3x+y≤ 600

x+y ≤ 300

x-y ≥ -100

x ≥ 0, y ≥ 0