Q. 41

# A company manufacture two types of toys A and B. type A requires 5 minutes each for cutting and 10 minutes for each assembling. Type B requires 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours available for cutting and 4 hours available for assembling in a day. He earns a profit of ₹50 each on type A and ₹60 each on type B. How many toys of each type should the company manufacture in a day to maximize the profit?

Let the company manufacture x and y numbers of toys A and B.

According to the question,

5X + 8y

Maximize Z = 50x + 60y

The feasible region determined 5X + 8y is given by

The corner points of feasible region are A(0,0) , B(0,22.5) , C(12,15) , D(24,0).The value of Z at corner point is

The maximum value of Z is1500 and occurs at point (12,15).

The company should manufacture 12 A toys and 15 B toys to earn profit of rupees 1500.

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