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.

Answer 1

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

Let Z be total revenue

Here, Z = 100x + 120y ....(i)

Subjects to constraints:

Also 2x + 3y ≤ 30 ....(ii)

3x + y ≤ 17 ....(iii)

x, y ≥ 0 ....(iv)

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

For coordinate 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:

Therefore, maximum revenue is Rs 1, 260 when 3 workers and 8 units capital are used for production.