Question

Vitamins a and b are found in foods f\ and f2. One unit of f\ contains 3 units of vitamin a and 4 units of vitamin
b. One unit of f2 contains 6 units of vitamin a and 3 units of vitamin
b. One unit of f, and f2 costs rs. 4 and rs. 5 resp. The minimum daily requirement per person of a and b is 80 units and 100 units resp. Assuming that anything in excess of the daily minimum requirement of vitamin a and b is not harmful. Formulate an lpp and find the mix of f 1 and f2 at the minimum cost, also find the minimum cost.

Answer 1

Explanation:

Let required quantity of food F1 be x units and quantity of food F2 be y units.

Given, costs of one unit of food F1 and F2 are Rs 5 and Rs 2.5 respectively, so costs of x units of food F1 and y units of food F2 are Rs 5x and Rs 2.5y respectively.

Let Z be the total cost, so

Z = 5x + 2.5y

Given, one unit of food F1 and food F2 contain 2 and 4 units of vitamin A respectively, so x unit of Food F1 and y units of food F2 contain 2x and 4y units of vitamin A respectively, but minimum requirement of vitamin A is 40 unit, so

2x + 4y ≥ 40 (First constraint)

Given, one unit of food F1 and food F2 contain 3 and 2 units of vitamin B respectively, so x unit of Food F1 and y units of food F2 contain 3x and 2y units of vitamin B respectively, but minimum daily requirement of vitamin B is 40 unit, so

3x + 2y ≥ 50 (Second constraint)

Hence, mathematical formulation of LPP is,

Find x and y which

Minimize Z = 5x + 2.5y

Subject to constraint,

2x + 4y ≥ 40

3x + 2y ≥ 50

x, y ≥ 0 [Since requirement of food F1 and F2 cannot be less zero.]