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]*

*[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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PREVIOUSTwo tailors, A and B earn ₹ 300 and ₹ 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.[CBSE 2017]NEXTMaximise z = x + 2y
Subject to the constraints
x + 2y ≥ 100
2x – y ≤ 0
2x + y ≤ 200
x, y ≥ 0
Solve the above LPP graphically. [CBSE 2017]

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