Lecture 9  Outline
1
Lecture 9: Linear Programming (Textbook:
Supplement E)
Objectives
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Basic Concepts
z
Formulation
z
Computer Solution
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Sensitivity Analysis
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Transportation/Transshipment Modeling
Basic Concepts and Formulation
Linear programming is an optimization process

A single objective function states mathematically what is being
maximized or minimized

Decision variables represent choices that the decision maker can
control

Constraints are limitations that restrict the decision variables. One of
three types:
≤
,
≥
, =

The feasible region

Parameter or a coefficient

Linear objective function and constraints

Nonnegativity
Formulating a Problem
°
Step 1. Define the Decision Variables.
°
Step 2.Write Out the Objective Function.
°
Step 3. Write Out the Constraints.
As a consistency check, make sure the same unit of measure is being used on both
sides of each constraint and the objective function
Problem 1 (Example E.1):
The Stratton Company produces 2 basic types of plastic
pipe. Three resources are crucial to the output of pipe: extrusion hours, packaging
hours, and a special additive to the plastic raw material. Below is next week’s situation.
All data are expressed in units of 100 feet of pipe. The contribution to profits and
overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2. Formulate a linear
programming model to determine how much of each type of pipe should be produced to
maximize contribution to profits and to overhead.
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Lecture 9  Outline
2