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. The profit on a necklace is ₹100 and that on a bracelet is ₹300. Formulate an LPP 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 & explanation
Correct answer: option 1
The correct answer is Option (1) → Maximize $Z = 100x + 300y$, Subject to: $x + y \leq 24, \enspace x + 2y \leq 32, \enspace x \geq 1, \enspace y \geq 1$ ##
Let $x$ necklaces and $y$ bracelets be manufactured.
$∴$ LPP is Maximise profit,
$Z = 100x + 300y$
Subject to constraints
$x + y \leq 24$
$\frac{1}{2}x + y \leq 16 \quad \text{or} \quad x + 2y \leq 32$
$x, y \geq 1$