Model 2: Pig Farming

A farmer is raising pigs for market, and he wishes to determine the quantities of the available types of feed that should be given to each pig to meet certain nutritional requirements at a minimum cost. The number of units of each type of basic nutritional ingredient contained within a kilogram of each feed type is given in the following table, along with the daily nutritional requirements and feed costs:

Nutritional ingredient		Kilogram of corn	Kilogram of tankage	Kilogram of alfalfa	Minimum daily requirement
Carbohydrates Protein Vitamins		90 30 10	20 80 20	40 60 50	200 180 150
Cost (in cents)		35	30	25

Formulate the linear programming model for this problem.

Decision Variables: F_i = Kg food type i=1,2,3 to give each pig

Objective: Minimize Cost = 35 F₁ + 30 F₂ + 25 F₃

Constraints:

Carbohydrates: 90 F₁ + 20 F₂ + 40 F₃ >= 200
Proteins: 30 F₁ + 80 F₂ + 60 F₃ >= 180
Vitamins: 10 F₁ + 20 F₂ + 50 F₃ >= 150

Non-negativity: 0 <= F_i, i=1,2,3