Question

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 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 maximise the profit? It is being given that at least one of each must be produced.​

Answer 1

Step-by-step explanation:

Let x be the number of necklaces manufactured and y be the number of bracelets manufactured. The total number of necklaces and bracelets it can handle is at most 24, so, according to the question,

x+y≤24

The x items take x hours to manufacture and y items take 2y hours to manufacture and the maximum time available is for 16 hours. So,

x+2y≤16

The profit on one necklace is given as Rs100 and the profit on one bracelet is given as Rs300.

Let the profit be z. To maximize the profit,

z=100x+300y

Therefore, the required constraints is,

z=100x+300y

Subject to the constraints,

x+y≤24

x+2y≤16

Answer 2

Answer:

Your answer is given above

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