Linear programming is a widely used model type that can solve
decision problems with many thousands of variables. Generally,
the feasible values of the decisions are delimited by a set
of constraints that are described by mathematical functions
of the decision variables. The feasible decisions are compared
using an objective function that depends on the decision variables.
For a linear program the objective function and constraints
are required to be linearly related to the variables of the
The examples in this section illustrate that linear programming
can be used in a wide variety of practical situations. We illustrate
how a situation can be translated into a mathematical model,
and how the model can be solved to find the optimum solution.