# A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 hours

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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  8,000 and 12,000 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.

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Let the number of pieces of model A to be manufactured be x and the number of pieces of model B to be manufactured be y.

Then LPP is maximize P = 8,000 x + 12,000 y

Hence, the number of pieces of model A = 12, the number of pieces of model B = 6 and the maximum profit = ₹ 1,68,000.