Question

A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 in magazines A and B per copy. These are processed on three Machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II, and 2 hours on machine III. Magazine B requires 3 hours on machine I, 2 hours on machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, and 60 hours per week respectively. Formulate the LPP to determine weekly production of magazines A and B, so that the total profit is maximum.

Answer 1

Let the company prints x magazine of type A and y magazine of type B.

Profit on sale of magazine A is ₹ 10 per copy and magazine B is ₹ 15 per copy. Therefore, the total earning z of the company is z = ₹(10x + 15y).

This is a linear function that is to be maximized. Hence, it is an objective function.

The constraints are as per the following table:

Magazine type →	Time required per unit		Available time per week (in hours)
Machine type ↓	Magazine A (x)	Magazine B (y)
Machine I	2	3	36
Machine II	5	2	50
Machine III	2	6	60

From the table, the total time required for Machine I is (2x + 3y) hours, for Machine II is (5x + 2y) hours and Machine III is (2x + 6y) hours. 

The machines I, II, III are available for 36, 50, and 60 hours per week. Therefore, the constraints are 2x + 3y ≤ 36, 5x + 2y ≤ 50, 2x + 6y ≤ 60.

Since x and y cannot be negative. We have, x ≥ 0, y ≥ 0. Hence, the given LPP can be formulated as:

Maximize z = 10x + 15y, subject to

2x + 3y ≤ 36,  5x + 2y ≤ 50,  2x + 6y ≤ 60, x ≥ 0, y ≥ 0.