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Chapter 7: Problem 21

What is a constraint in a linear programming problem? How is a constraint represented?

Short Answer

Expert verified
A constraint in linear programming is a condition imposed on the variables of the problem that need to be satisfied. It is represented as a linear equation or inequality involving these variables.

Step by step solution

01

Understanding a Constraint

A constraint in linear programming refers to a condition that must be satisfied in an optimization or decision-making problem. It is an equality or inequality that defines the feasible solution space in which an optimal solution (if it exists) must lie.
02

Representation of a Constraint

In linear programming, we assign variables to the quantities we want to optimize. These quantities depend on the context of the problem. A constraint is usually represented as a linear equation or inequality involving these variables. For instance, if we are optimizing quantities x and y, a constraint could be an equation or inequality such as \( x + 2y \leq 10 \) or \( 3x - y = 5 \). The coefficients in the equations, as well as the restriction (inequality or equality), are determined by the specifics of the problem.

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