Question

A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours. On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.

Answer 1

Let the company manufactures x boxes of type A screws and y boxes of type B screws.

From the given information, we can construct the following table.

Items	Type A (x)	Type B (y)	Minimum time available on each machine in a week
Time required on threading machine	2	8	60 × 60 = 3600 minutes
Time required on slotting machine	3	2	60 × 60 = 3600 minutes
Profit	₹ 100	₹ 170

As per the information in the above table, the objective function for maximum profit Z = 100x + 170y

Subject to the constraints

2x + 8y ≤ 3600 ⇒ x + 4y ≤ 1800  ......(i)

3x + 2y ≤ 3600  ......(ii)

x ≥ 0, y ≥ 0  ......(Non-negative constraints)

Hence, the required LPP is

Maximise Z = 100x + 170y

Subject to the constraints,

x + 4y ≤ 1800, 3x + 2y ≤ 3600, x ≥ 0, y ≥ 0.