Q. 2

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and a 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. Formulate on L.P.P. for finding 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. [CBSE 2017]

Answer :

Let x necklaces and y bracelets manufactured by a small firm.

Our problem is to maximise Z = 100x + 300y

subject to constraints are

x + y + ≤ 24,

and x ≥ 0, y ≥ 0

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