Question

Producer Rahul has 50 and 85 units of labour and capital respectively which he can use to produce two types of goods A and B. To produce one unit of A, 1 unit of labour and 2 units of capital are required. Similarly 3 units of labour and 2 units of capital is required to produce 1 unit of B. If A and B are priced at Rs 100 and Rs 150 per unit respectively, how should the producer use his resources to maximize the total revenue. Formulate the L.P.P. to maximize his total revenue?

Answer 1

Let the units of product A be x and product B be y

	Labour	Capital	Price
A	1	2	100
B	3	2	150
Limitations available	50	85

Maximize z = 100 x + 150 y 

subject to the restrictions 

x + 3y ≤ 50 

2x + 2y ≤ 85 

x,y ≥ 0