A shopkeeper buys fans at ₹300 and lamps at ₹150, with ₹6,000 to spend and room for 30 items. He makes ₹40 on a fan and ₹25 on a lamp. What is his largest possible profit?

Explanation

1. 01

   With $x$ fans and $y$ lamps: $300x + 150y \le 6{,}000$, that is $2x + y \le 40$, and $x + y \le 30$; maximise $Z = 40x + 25y$.

2. 02

   Corners: $(0, 0)$, $(0, 30)$, $(10, 20)$, $(20, 0)$, where $Z$ is $0$, $750$, $900$, $800$.

3. 03

   The largest is ₹900, with 10 fans and 20 lamps.