Q2 of 17 Page 12

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]

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


More from this chapter

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1

Two 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]

 3

Maximise 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]

 4

Solve the following L.P.P. graphically :

Minimize


Subject to


Constraints



and [CBSE 2017]

5

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.[CBSE 2011]