Q26 of 26 Page 1

A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing. Each piece of model B requires 12 hours of labour for fabricating and 3 hours for finishing. The maximum number of labour hours, available for fabricating and for finishing, are 180 and 30 respectively. The company makes a profit of Rs 8000 and Rs 12000 on each piece of model A and model B respectively. How many pieces of each model should be manufactured to get maximum profit? Also, find the maximum profit.

Given Data:


• Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing.


• Each piece of model B requires 12 hours of labour for fabricating and 3 hours for finishing.


• The maximum number of labour hours, available for fabricating is 180


• The maximum number of labour hours, available for finishing is 30


• The company makes a profit of Rs 8000 and Rs 12000 on each piece of model A and model B respectively


Calculation:


Let x and y be the number of models A and models B to be manufactured respectively.


Now the profit function is P = 8000x + 12000y


We have to maximize the profit


The constraints in this situation are:


• Quantities x and y are positive


x ≥ 0; y ≥ 0


• Maximum no. of labour hours for fabricating


9x + 12y ≤ 180 or 3x + 4y ≤ 60


• Maximum no. of labour hours for finishing


x + 3y ≤ 30



We need to check at each corner points for maximum profit. Corner points in this LPP problems are (0, 0), (20,0), (0,10) and (12,6)


Profit at (0, 0),


P = 8000×0 + 12000×0 = 0


Profit at (20, 0),


P = 8000×20 + 12000×0 = Rs.1,60,000


Profit at (0, 10),


P = 8000×0 + 12000×10 = Rs.1,20,000


Profit at (12, 6),


P = 8000×12 + 12000×6 = Rs.1,68,000 (maximum)


For maximum profit 12 pieces of model A and 6 pieces of model B are to be manufactured with maximum profit of Rs.1,68,000.


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