Introduction to Linear Programming BSAD 141 Dave Novak

Topics Covered Discussion of Linear Programming Example handout

Linear Programming Linear – a linear relationship exists between variables (like our regression example) Program – a set of steps is followed to solve the model

The LP Model 1) Decision variables (x 1, x 2,… x i ) Typically represent quantities of something What are the “optimal” values of x 1, x 2 ? 2) Objective Function (OF): the linear equation describing the mathematical relationship between the decision variables Only 1 OF The expression we are maximizing or minimizing

The LP Model 3) Constraints: linear equations expressing values the decision variables (x 1, x 2 ) can or cannot take on Restrictions or conditions that apply to the problem For example, resource limitations like labor, materials, production capacity, etc. Nonnegativity constraints

Discussion Consider the question of how many trucks should be made by Ford What is a problem definition or objective? What are some decision variables What are some constraints? If profit increases based on the number of trucks sold, Ford would want to make an unlimited number of trucks… We have to impose realistic constraints

Irregular Problems May not always be a “best” solution Multiple optimal solutions Infeasible solution No values of (x 1, x 2 ) satisfy all constraints at the same time Unbounded solution Solution space for a Max problem is not bounded

When to use LP The decision involves minimizing or maximizing something The decision involves questions about how much or how many You have constraints on the decision variables Labor Input materials Production limitations

Example See the handout