Algorithms Analysis Practice Test 2025 - Free Algorithms Practice Questions and Study Guide

In linear programming, constraints often need to be represented as inequalities because they define the feasible region within which a solution must fall. This feasibility region is bounded by these inequalities, which restrict the values that decision variables can take. For example, a constraint like \(x + y \leq 10\) indicates all combinations of \(x\) and \(y\) that satisfy this condition, including points on the line and below it in a two-dimensional space.

While some constraints can be expressed as equalities (for instance, when specifying limits or exact requirements), representing a constraint as an inequality is essential to encompass a broader range of possible solutions. This is particularly relevant in optimization problems where there can be multiple feasible solutions that still satisfy all constraints.

Thus, maximizing or minimizing an objective function is typically approached by exploring this region defined by inequalities. Ultimately, the requirement for constraints to be represented as inequalities allows for more flexible and practical modeling of real-world situations in linear programming.