Raunak is a small-scale entrepreneur who sells sewing machines in a rural market. He wants to…
Raunak is a small-scale entrepreneur who sells sewing machines in a rural market. He wants to expand his business but has two main constraints: Capital and Storage.
He has a total capital of ₹5,760 to invest. The godown can store a maximum number of 20 sewing machines.
Raunak sells two types of machines:
- Electronic sewing machine, each costs him ₹360.
- Manually operated sewing machine, each costs him ₹240.
His wife Radhika suggests selling an electronic machine at a profit of ₹22 and a manually operated sewing machine at a profit of ₹18.
Using the concept of Linear Programming Problem, find the number of sewing machines of each type that Raunak should sell to maximise his profit.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Let $x$ and $y$ denote the number of electronic and manually operated sewing machines respectively.
Constraints:
$x + y \le 20$ (Storage constraint)
$360x + 240y \le 5760 \implies 3x + 2y \le 48$ (Capital constraint)
$x \ge 0, y \ge 0$, and $x, y \in \mathbb{Z}$
Objective function: Maximize profit $Z = 22x + 18y$.
Evaluating $Z$ at the vertices of the feasible region:
1. $(0, 0): Z = 0$
2. $(0, 20): Z = 22(0) + 18(20) = 360$
3. Intersection of $x + y = 20$ and $3x + 2y = 48$:
$x = 8, y = 12 \implies Z = 22(8) + 18(12) = 176 + 216 = 392$.
4. $(16, 0): Z = 22(16) + 18(0) = 352$.
Maximum profit is ₹392, obtained when $x = 8$ and $y = 12$.
Therefore, Raunak should sell 8 electronic sewing machines and 12 manually operated sewing machines to maximise his profit.
From ISC 2026 Mathematics Paper 1, question 22.