CUET Preparation Today
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. |
Maximize $Z = 100x + 300y$, Subject to: $x + y \leq 24, \enspace x + 2y \leq 32, \enspace x \geq 1, \enspace y \geq 1$ Maximize $Z = 300x + 100y$, Subject to: $x + y \geq 24, \enspace x + 2y \geq 32, \enspace x \geq 0, \enspace y \geq 0$ Maximize $Z = 100x + 300y$, Subject to: $x + y \leq 24, \enspace 2x + y \leq 16, \enspace x \geq 1, \enspace y \geq 1$ Maximize $Z = 100x + 300y$, Subject to: $x + y \leq 32, \enspace x + 2y \leq 24, \enspace x \geq 1, \enspace y \geq 1$ |
Maximize $Z = 100x + 300y$, Subject to: $x + y \leq 24, \enspace x + 2y \leq 32, \enspace x \geq 1, \enspace y \geq 1$ |
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 $x + y \leq 24$ $\frac{1}{2}x + y \leq 16 \quad \text{or} \quad x + 2y \leq 32$ $x, y \geq 1$ |
