Q43 of 97 Page 1376

A manufacturing company makes two types of teaching aids A and B of mathematics for class XII. Each type of A requires 9 labor hours of fabricating and 1 labor hour for finishing. Each type of B requires 12 labors hour for fabricating and 3 labor hour for finishing. For fabricating and finishing, the maximum labor hours available per week are 180 and 30 respectively. The company makes a profit of ₹80 on each piece of type A and ₹120 on each piece of type B. how many pieces of type A and 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 LLP and solve graphically. What is the maximum profit per week?


Let the company make x no of 1st type of teaching aid and y no of 2nd type of teaching aid.


∴According to the question,


9x + 12y


Maximize Z = 80x + 120y


The feasible region determined by 9x + 12y is given by



The corner points of feasible region are A(0,0) , B(0,10) , C(12,6) , D(20,0).The value of Z at corner point is



The maximum value of Z is 1680 and occurs at point (12,6).


The company should make 12 of 1st type and 6 of 2nd type of teaching aid. Maximum profit is Rs.1680.


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A manufacturing company makes two types of teaching aids A and B of mathematics for class XII. Each type of A requires 9 labor hours of fabricating and 1 labor hour for finishing. Each type of B requires 12 labors hour for fabricating and 3 labor hour for finishing. For fabricating and finishing, the maximum labor hours available per week are 180 and 30 respectively. The company makes a profit of ₹80 on each piece of type A and ₹120 on each piece of type B. how many pieces of type A and 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 LLP and solve graphically. What is the maximum profit per week?