Question

Food F₁ contains 2, 6, 1 units and food F₂ contains 1, 1, 3 units of proteins, carbohydrates, fats respectively per kg. 8, 12 and 9 units of proteins, carbohydrates and fats is the weekly minimum requirement for a person. The cost of food F₁ is Rs. 85 and food F₂ is Rs. 40 per kg. Formulate the L.P.P. to minimize the cost.

Answer 1

Let Z be the cost of food F₁ and F₂ purchased.

Let x kg. of food F₁ and y kg. of food F₂ be purchased to meet the minimum requirement.

Since the costs of food F₁ and F₂ are Rs. 85 and Rs. 40 per kg,

∴ Z = 85x + 40y and x ≥ 0, y ≥ 0

Content/Food	F1 x	F2 y	Minimum requirement
Protein	2	1	8
Carbohydrate	6	1	12
Fat	1	3	9

The constraints are:

2x + y ≥ 8, 6x + y ≥ 12, x + 3y ≥ 9

The L.P.P. is

Minimize Z = 85x + 40y

Subject to 2x + y ≥ 8

6x + y ≥ 12

x + 3y ≥ 9, x ≥ 0, y ≥ 0