Question

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A requires 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. Given that total time for cutting is 3 hours 20 minutes and for assembling 4 hours. The profit for type A souvenir is ₹ 100 each and for type B souvenir, profit is ₹ 120 each. How many souvenirs of each type should the company manufacture in order to maximize the profit? Formulate the problem as an LPP and solve it graphically.

Answer 1

Suppose number of souvenirs of type A and type B are x and y respectively.

Then, the LPP is as follows:

Maximize Z = 100x + 120y

Subject to 5x + 8y ≤ 200

10x + 8y ≤ 240

And x, y ≥ 0

To solve the LPP graphically first we convert inequalities into equations and draw the corresponding lines.

Then, 

Corner points	Value of Z in ₹
A (0, 25)	3000
B (8, 20)	3200 maximum
C (24, 0)	2400

Clearly, maximum profit is obtained when 8 souvenirs of type A and 20 souvenirs of type B is manufactured.

Then Maximum profit = 100 × 8 + 120 × 20 = ₹ 3200.