Question

Shreya company produces 2 types of shoes A and B. A is of superior type and B is of ordinary type. Each shoe of the first kind requires thrice as much time as the second kind. If all shoes are the second kind only, the company can produce a total of 650 pairs a day. Only a maximum of 150 pairs of the first kind and 400 of the second kind can be sold per day. If the profit per pair of the first kind is Rs 400 and per pair of the second kind is Rs 105. Find the optimal products mix to be produced to maximize the profit by formulating on L.P.P. model.

Answer 1

Let the number of units of shoe A be x and shoe B be y, time taken by shoe A is hours & time taken by shoe B is 1 hour company can produce 650 pairs per day 

∴ 3x + y ≤ 650 

Similarly maximum of 150 pairs of shoe A can be produced i.e x ≤ 150 and 400 of shoe B can be sold i.e. y ≤ 400 

Maximize z = 400x + 105y subject to the constraints 

3x + y ≤ 650 

x ≤ 150 

y ≤ 400 

x ≥ 0,y ≥ 0