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A manufacturing company makes two types of teaching aids A and B of Matematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finighing. Each type of B requires 12 labour orse for fabricating and 3 labour hours for finighsing. 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 ech 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 a LPP and solve graphically. What is the maximum profit per week ?

Answer»


Solution :Let the NUMBER of pieces of type A and type B manufactured per week be x and y RESPECTIVELY.
Then, we have to MAXIMIZE `P=80x+120y` subject to the constraints
`9x+12yle180implies3x+4yle60,""...(i)`
`x+3yle30""...(ii)`
and `x ge0,y ge0.`ltbegt We leave it to the reader to DRAW th graphs.
For maximum profit, we shall have 12 pieces of type A and 6 PICES of type B, and the maximum profit is Rs. 1680.


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