Problem 26 - College Algebra

Question

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

Step-by-Step Solution

Answer

In linear programming, a constraint is a restriction on the decision variables. They are represented mathematically as linear equations or inequalities.

Step 1: Define Constraint in Linear Programming

A constraint in a linear programming problem is a restriction or limitation imposed on a decision. In mathematical terms, it's an equation or inequality that define the conditions that the solution must satisfy. For instance, if we want to maximize profit in a production process, constraints could be the availability of raw material, labor hours etc. In simple words, constraints define the feasible region within which we search for the optimal solution.

Step 2: Representation of Constraint

Constraints are represented mathematically as linear equations or inequalities depending on the problem statement. For example, if we have a constraint that the total hours worked by an employee must be less than or equal to 40 hours per week, this can be represented as \(x \leq 40\), where \(x\) represents the total hours worked by an employee in a week.