A situation in which more than one optimal solution is possible. It arises when the slope of the objective function is the same as the slope of a constraint.

A constraint with zero slack or surplus for the optimal solution.

A restriction on the resources available to a firm (stated in the form of an inequality or an equation).

A point that lies on one of the corners of the feasible region. This means that it falls at the intersection of two constraint lines.

The method of finding the optimal solution to an LP problem by testing the profit or cost level at each corner point of the feasible region. The theory of LP states that the optimal solution must lie at one of the corner points.

A variable whose value may be chosen by the decision maker.

The improvement in the objective function value that results from a one-unit increase in the right-hand side of that constraint.

The area satisfying all of the problem’s resource restrictions—that is, the region where all constraints overlap. All possible solutions to the problem lie in the feasible region.

A point lying in the feasible region. Basically, it is any point that satisfies all of the problem’s constraints.

A mathematical expression containing a greater-than-or-equal-to relation $(\ge )$ or a less-than-or-equal-to relation $(\le )$ used to indicate that the total consumption of a resource must be $\ge$ or $\le$ some limiting value.

Any point lying outside the feasible region. It violates one or more of the stated constraints.

A straight line representing all combinations of $X_1$ and $X_2$ for a particular cost level.

A straight line representing all nonnegative combinations of $X_1$ and $X_2$ for a particular profit level.

A mathematical technique used to help management decide how to make the most effective use of an organization’s resources.

The general category of mathematical modeling and solution techniques used to allocate resources while optimizing a measurable goal. LP is one type of programming model.

A constraint with a positive amount of slack or surplus for the optimal solution.

A set of constraints that requires each decision variable to be nonnegative; that is, each $X_i$ must be greater than or equal to 0.

A mathematical statement of the goal of an organization, stated as an intent to maximize or to minimize some important quantity such as profits or costs.

A common LP problem involving a decision as to which products a firm should produce given that it faces limited resources.

The presence of one or more constraints that do not affect the feasible solution region.

The study of how sensitive an optimal solution is to model assumptions and to data changes. It is often referred to as postoptimality analysis.

The increase in the objective function value that results from a one-unit increase in the right-hand side of that constraint.

The difference between the left-hand side and the right-hand side of a less-than-or-equal-to constraint. Often this is the amount of a resource that is not being used.

The difference between the left-hand side and the right-hand side of a greater-than-or-equal-to constraint. Often this represents the amount by which a minimum quantity is exceeded.

Coefficients of the variables in the constraint equations. The coefficients represent the amount of resources needed to produce one unit of the variable.

A condition that exists when a solution variable and the profit can be made infinitely large without violating any of the problem’s constraints in a maximization process.