Question

A manufacturing company makes two types of teaching aids A and B of mathematics for class XII. Each type of Arequires 9 labour hours for fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30, respectively. The company makes a profit of Rs 80 on each piece of type A and Rs 120 on each piece of type B. How many pieces of type A and B should be manufactured per week to get a maximum profit? What is the maximum profit per week?

Answer 1

Let x and y be the number of pieces of type A and B manufactured per week respectively. If Z be the profit then,

Objective function, Z = 80x + 120y ...(i)

We have to maximize Z, subject to the constraints

9x + 12y ≤ 180

3x + 4y ≤ 60 ...(ii)

x + 3y ≤ 30 ...(iii)

x ≥ 0, y ≥ 0 ...(iv)

The graph of constraints are drawn and feasible region OABC is obtained, which is bounded having corner points O (0, 0), A(20, 0), B (12, 6) and C (0, 10)

Now the value of objective function is obtained at corner points as

Hence, the company will get the maximum profit of Rs 1,680 by making 12 pieces of type A and 6 pieces of type B of teaching aid.