Question

A diet for a sick person must contain atleast 4000 units of vitamins, 50 units of minerals and 1400 units of calories. Two foods A and B are available at a cost of Rs 5 and Rs 4 per unit respectively. One unit of the food A contains 200 units of vitamins, 1 unit of minerals and 40 units of calories while one unit of food B contains 100 units of vitamin, 2 units of minerals and 40 units of calories. Find what combination of the food A and B should be used to have least cost but it must satisfy the requirement of the sick person. Form LPP and solve graphically.

Answer 1

Let x unit of food A and y unit of food B are mixed. 

Objective function is minimise cost Z = 5x + 4y 

Subject to constraints are 

200x + 100y ≥ 4000 ⇒ x + 2y ≥ 50 

40x + 40y ≥ 1400 ⇒ x, y ≥ 0

Here solution set is unbounded. So minimum value Rs 145 may or may not be occur. 

Take 5x + 4y < 145 

Plot this by dotted line. Open half plane determined by 5x + 4y < 145 do not have a point common, so Rs 145 is the minimum value when 5 units of food A and 30 units of food B are mixed.