Optimization and Objective Function

CHAPTER 2

An Introduction to
Linear Programming

21
KEY CONCEPTS

ILLUSTRATED ANSWERED
CONCEPT PROBLEMS PROBLEMS

Formulation 7,8 15,16

Minimization 2,5 9,10,15

Standard Form 1 14

Slack/Surplus Variables 1 16

Equal-to Constraints 3,5 14

Redundant Constraints 5,7 12,13

Extreme Points 2,5 11,16

Alternative Optimal Solutions 7 10,11,15

Infeasibility 4 14

Unbounded 4 11

Spreadsheet Example 2

REVIEW

1. A mathematical programming problem is one that seeks to maximize an objective function subject to constraints. If both the objective function and the constraints are linear, the problem is referred to as a linear programming problem.

2. Linear functions are functions in which each variable appears in a separate term raised to the first power and is multiplied by a constant (which could be 0).

3. Linear constraints are linear functions that are restricted to be "less than or equal to", "equal to", or "greater than or equal to" a constant.

4. The maximization or minimization of some quantity is the objective in all linear programming problems.

5. A feasible solution satisfies all the problem's constraints.

6. A linear program which is