Introduction to Linear Programming BSAD 141 Dave Novak.
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Transcript of Introduction to Linear Programming BSAD 141 Dave Novak.
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 (x1, x2,… xi)Typically represent quantities of something What are the “optimal” values of x1, x2?
2) Objective Function (OF): the linear equation describing the mathematical relationship between the decision variables Only 1 OFThe expression we are maximizing or
minimizing
The LP Model 3) Constraints: linear equations expressing
values the decision variables (x1, x2) can or cannot take on
Restrictions or conditions that apply to the problemFor example, resource limitations like labor,
materials, production capacity, etc.Nonnegativity constraints
Discussion Consider the question of how many trucks
should be made by FordWhat is a problem definition or objective?What are some decision variablesWhat 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 solutionsInfeasible solution
• No values of (x1, x2) 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
variablesLaborInput materialsProduction limitations
Example See the handout