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 Rs. 100 and that on a bracelet is Rs. 300, formulate an L.P.P. for finding how many of each should be produced daily to maximize the profit. It is given that at least one of each must be produced.
Answer: Maximize P = 100x + 300y subject to x + y ≤ 24, x + 2y ≤ 32, x ≥ 1, y ≥ 1
Solution
Let necklaces and bracelets be produced per day.
Profit to maximise: .
Total number:
Time:
At least one of each:
This is the required formulation of the L.P.P.:
Profit to maximise: .
Total number:
Time:
At least one of each:
This is the required formulation of the L.P.P.:
CBSE Class 12 Board · 2017 · Subjective