Question

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximise the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?

Answer 1

Let x, y unit of goods A and B are produced respectively. 

Let Z be total revenue 

Here Z = 100x + 120y ....(i) 

Also 2x + 3y ≤ 30 ....(ii) 

3x + y ≤ 17 ....(iii) 

x ≥ 0 ....(iv) 

y ≥ 0 ....(v) 

On plotting graph of above constants or inequalities (ii), (iii), (iv) and (v). We get shaded region as feasible region having corner points A, O, B and C.

For co-ordinate of 'C' 

Two equations (ii) and (iii) are solved and we get coordinate of C = (3, 8) 

Now the value of Z is evaluated at corner point as:

Corner points	Z = 100x + 120y
(0, 10)	1200
(0, 0)	0
(17/3, 0)	1700/3
(3, 8)	1260 Maximum

Therefore maximum revenue is Rs. 1,260 when 2 workers and 8 units capital are used for production. Yes, although women workers have less physical efficiency but it can be managed by her other efficiency.