Food X costs ₹50 a kg and gives 1 unit of vitamin A and 2 of vitamin B per kg; food Y costs ₹70 a kg and gives 2 units of A and 1 of B. A mix needs at least 8 units of A and 10 of B. What is the least cost?

Explanation

1. 01

   With $x$ kg of X and $y$ kg of Y: $x + 2y \ge 8$, $2x + y \ge 10$; minimise $Z = 50x + 70y$.

2. 02

   Corners: $(0, 10)$, $(4, 2)$, $(8, 0)$, where $Z$ is $700$, $340$, $400$.

3. 03

   $50x + 70y < 340$ has no point in the region, so the least cost is ₹340, with 4 kg of X and 2 kg of Y.