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in Linear Programming by (27.7k points)
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A manufacture makes two product, A and B. product A sells at ₹200 each and takes \(\frac{1}{2}\) hour to make. Product B sells at ₹300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than ₹10000. If the profit on each of the product A is ₹20 and on product B, it is ₹30 then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.

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Let x and y be number of A and B products. 

∴According to the question, 

0.5x + y ≤ 40, 200x + 300y ≥ 10000, x ≥ 14, y ≥ 16 

Maximize Z = 20x + 30y 

The feasible region determined by 0.5x + y ≤ 40, 200x + 300y ≥ 10000, x ≥ 14, y ≥ 16 is given by

The corner points of feasible region are A(14,33) , B(14,24) , C(26,16), D(48,16).

The value of Z at corner points are

Corner Point Z = 20x + 30y
A(14, 33) 1270
B(14, 24) 1000
C(26, 16) 1000
D(48, 16) 1440 Maximum

The maximum value of Z is 1440 at point (48,16). 

Hence, the manufacturer should manufacture 48 A products and 16 B products to maximize their profit of Rs.1440.

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