Question

Diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1500 calories Two foods F₁ and F₂ cost Rs. 50 and Rs. 75 per unit respectively. Each unit of food F₁ contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas each unit of food F₂ contains 100 units of  vitamins, 2 units of minerals and 30 calories. Formulate the above problem as L.P.P. to satisfy the sick person's requirements at minimum cost.

Answer 1

Let x₁ : Number of units of Food F₁
x₂ : Number of units of food F₂
Since the number of unit of foods cannot be negative.

∴ x₁ ≥ 0 and x₂ ≥ 0

Product	Food F1	Food F2	Minimum Requirement
Vitamins	200	100	4000
Minerals	1	2	50
Calories	40	30	1500
Cost per unit	Rs. 50	Rs. 75	-

From the table 
For vitamins 200x₁ + 100x₂ ≥  4000
For Minerals x₁ + 2x₂ ≥ 50
For Calories 40x₁ + 30x₂ ≥ 1500
Total cost  z = 50x₁ + 75x₂
∴ The L.P.P. is :
Minimize Z = 50x₁ + 75x₂
Subject to the constraints
200x₁ + 100x₂ ≥ 4000
x₁ + 2x₂ ≥ 50
40x₁ + 30x₂ ≥ 1500 and x₁ , x₂ ≥ 0