Question

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of 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 per week 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 type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. 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 

We have to maximize Z, subject to the constraints 

9x + 12y ≤ 180 ⇒ 3x + 4y ≤ 60 ...(i) 

x + 3y ≤ 30 ...(ii) 

x ≥ 0, y ≥ 0 ...(iii) 

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

Corner point	Z = 80x + 12y
O(0, 0)	0
A(20, 0)	1600
B(12, 6)	1680 Maximum
C(0, 10)	1200

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. Yes, teaching aid is necessary for teaching learning process as 

(i) it makes learning very easy. 

(ii) it provides active learning. 

(iii) students are able to grasp and understand concept more easily and in active manner.