A company makes two products, P and Q, earning ₹30 and ₹40 a unit. Each unit of P uses 1 hour of machine time and each unit of Q 2 hours; 40 hours are available. At most 30 units can be made in all. What is the largest profit, in rupees?

Explanation

1. 01

   With $x$ of P and $y$ of Q: maximise $Z = 30x + 40y$ subject to $x + 2y \le 40$, $x + y \le 30$, $x, y \ge 0$.

2. 02

   At the corners: $(0, 0) \to 0$, $(30, 0) \to 900$, $(20, 10) \to 1000$, $(0, 20) \to 800$.

3. 03

   The largest profit is ₹1,000, making 20 of P and 10 of Q.