Quantitative Techniques: Theory and Problems

DIET PROBLEM

Problem 1.78

The vitamins V and W are found in two different foods, F₁ and F₂. The respective prices per unit of each food are Rs. 3 and Rs. 2.5. One unit of F₁ contains 2 units of vitamin V and 3 units of vitamin W. Similarly one unit of F₂ contains 4 units of vitamin V and 2 units of vitamin W. Daily requirements of vitamin V is at least 60 units and vitamin W at least 75 units.

The problem is to determine optimal quantities of foods F₁ and F₂ to be bought so that the daily vitamin requirements are met and, simultaneously the cost of buying the foods is minimised.

Solution

Let x₁ and x₂ be the quantities of F₁ and F₂ respectively.

	Minimise 3x1 + 2.5x2
	Subject to 2x1 + 4x2 ≥ 60	(Minimum Requirements of Vitamin V)
	3