Q. 8

# A small firm manufactures necklace and bracelets. The total number of necklace and bracelet that it can handle per day is at most 24. It takes 1 hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ₹100 and that on a bracelet is ₹300, how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

Let the firm manufacture x number of necklaces and y number of bracelets a day.

According to the question,

X + y , 0.5x + y x

Maximize Z = 100x + 300y

The feasible region determined by X + y , 0.5x + y xis given by

The corner points of the feasible region are A(1,1) , B(1,15.5) , C(16,8) , D(23,1).The number of bracelets should be whole number. Therefore, considering point (2,15). The value of Z at corner point is

The maximum value of Z is 4700 at point B(2,15).

The firm should make 2 necklaces and 15 bracelets.

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