# Reference

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Chapter 7
Linear Programming: Maximization Models

Introduction
 Many management decisions involve trying to

make the most effective use of limited resources
 Machinery, labor, money, time, warehouse space, raw

materials

 Linear programming (LP) is a widely used

mathematical modeling technique designed to help managers in planning and decision making relative to resource allocation  Belongs to the broader field of mathematical programming  In this sense, programming refers to modeling and solving a problem mathematically

Requirements of a Linear Programming Problem
 LP has been applied in many areas over the past

50 years  All LP problems have 4 properties in common
1. All problems seek to maximize or minimize some quantity (the objective function) 2. The presence of restrictions or constraints that limit the degree to which we can pursue our objective 3. There must be alternative courses of action to choose from 4. The objective and constraints in problems must be expressed in terms of linear equations or inequalities

7–3

LP Properties and Assumptions
PROPERTIES OF LINEAR PROGRAMS
1. One objective function 2. One or more constraints 3. Alternative courses of action 4. Objective function and constraints are linear ASSUMPTIONS OF LP 1. Certainty 2. Proportionality 3. Additivity 4. Divisibility 5. Nonnegative variables
Table 1

Basic Assumptions of LP
 We assume conditions of certainty exist and

numbers in the objective and constraints are known with certainty and do not change during the period being studied We assume proportionality exists in the objective and constraints We assume additivity in that the total of all activities equals the sum of the individual activities We assume divisibility in that solutions need not…...

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