A dietician wishes to mix two types of foods in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 units/kg of vitamin C while Food II contains 1unit/kg of vitamin A and 2 units/kg of vitamin C. It costs ₹ 5 per kg to purchase Food I and 7 per kg to purchase Food II. Determine the minimum cost of such a mixture. Formulate the above as a LPP and solve it graphically.

Let x & y denotes the units of Food 1 & 2 to be purchased respectively.

According to question, the above data can be expressed as-

Minimise: Z = 5x + 7y …Objective function

Subject to Constraints:

2x + y ≥ 8

x + 2y ≥ 10

x, y ≥ 0

On plotting the half planes the unbounded feasible region with corners A, E & D is obtained.

Z is going to be optimized only at the corner points.

So we check value of z only at corner points.

A (0,8) z = 5(0) + 7(8) = 56

B (2,4) z = 5(2) + 7(4) = 38 (min.)

C (10,0) z = 5(10) + 7(0) = 50

As per the graph, the unbounded region has a new equality,

5x + 7y < 38

This inequality has no common point with the previous mentioned equations,

Thus, the minimum cost is Rs. 38 when 2 units of Food 1 and 4 units of Food 2 are purchased.