A diet mixes food A ($x$ kg) costing ₹60 a kg and food B ($y$ kg) costing ₹80 a kg. It needs at least 8 units of protein (A gives 2 a kg, B gives 4) and at least 6 units of iron (A gives 3 a kg, B gives 1). What is the least cost of the diet, in rupees?

Explanation

1. 01

   Minimise $Z = 60x + 80y$ subject to $2x + 4y \ge 8$, $3x + y \ge 6$, $x, y \ge 0$: an unbounded region.

2. 02

   Corners: $(0, 6) \to 480$, $\left(\frac{8}{5}, \frac{6}{5}\right) \to 96 + 96 = 192$, $(4, 0) \to 240$.

3. 03

   The half-plane $60x + 80y < 192$ misses the region, so the least cost is ₹192.