Question

Imagine that the minimum weekly needs of a person in proteins, carbohydrates and fats are, respectively, 8, 12 and 9 units. Suppose we must obtain a preparation with that minimum composition by mixing two products A and B, whose contents per kilogram are those identified in the following table:

	Proteins	Hydrates	Fats	Cost/KG
A	2	6	1	600
B	1	1	3	400

How many kilograms of each product should be purchased weekly so that the cost of preparing the diet is minimal?

Pose and solve the previous problem as a linear programming model.

Answer 1

Objective function refers to the function that is either maximized or minimized. The constraints may be equalities or inequalities. So, in linear programming problems, linear objective functions are minimized or maximized which is subject to linear constraints. Thus, in a linear programming problem the objective function and the constraints must be linear functions of the decision variables.