Question

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 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. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs. 5 each for type A and Rs. 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?

Answer 1

P = 5x + 6y 

subject to the constraints

(i) 5x + 8y ≤ 200 

(ii) 10x + 8y ≤ 240 

⇒ 5x + 4y ≤ 120 

(iii) x ≥ 0; y ≥ 0

A (0,0) P = 5x + 6y = 0 

B (24,0) P = 5 x 24+ 6 x 0= 120 Rs 

C (8,20) P = 5 x 8 + 6 x 20 = 160 Rs 

D (0, 25) P = 5 x 0+ 6 x 25 = 150 Rs 

At C (8, 20) P is maximised to Rs 160 

∴ 8 types of A and 2 : 6 types of B