A variable that has no meaning in a physical sense but acts as a tool to help generate an initial LP solution.

A solution to an LP problem that corresponds to a corner point of the feasible region.

The set of variables that are in the solution, have positive, nonzero values, and are listed in the solution mix column.

The row containing the net profit or loss that will result from introducing one unit of the variable indicated in that column into the solution.

The basic feasible solution that is the set of variables presently in the solution. It corresponds to a corner point of the feasible region.

A condition that arises when there is a tie in the values used to determine which variable will enter the solution next. It can lead to cycling back and forth between two nonoptimal solutions.

The situation in which there is no solution that satisfies all of a problem’s constraints.

A process (algorithm) that repeats the same stpng over and over.

Variables not in the solution mix or ­basis. Nonbasic variables are equal to zero.

The column with the largest positive number in the $C_j-Z_j$ row of a maximization problem or with the largest negative $C_j-Z_j$ improvement value in a minimization problem. It indicates which variable will enter the solution next.

The number at the intersection of the pivot row and pivot column.

The row corresponding to the variable that will leave the basis in order to make room for the variable entering (as indicated by the new pivot column). This is the smallest positive ratio found by dividing the quantity column values by the pivot column values for each row.

An alternative way of stating an LP problem.

A column in the simplex tableau that gives the numeric value of each variable in the solution mix column.

The range of values over which a nonbasic variable’s coefficient can vary without causing a change in the optimal solution mix.

The range of values over which a basic variable’s coefficient can change without causing a change in the optimal solution mix.

A method used to find the range over which shadow prices remain valid.

The coefficients of slack variables in the $C_j-Z_j$ row. They represent the value of one additional unit of a resource.

A matrix algebra method for solving LP problems.

A table for keeping track of calculations at each iteration of the simplex method.

A variable added to less-than-or-equal-to constraints in order to create an equality for a simplex method. It represents a quantity of unused resource.

A column in the simplex tableau that contains all the basic variables in the solution.

The coefficients in the central body of each simplex table. They indicate the number of units of each basic variable that must be removed from the solution if a new variable (as represented at any column head) is entered.

A variable inserted in a greater-than-or-equal-to constraint to create an equality. It represents the amount of resource usage above the minimum required usage.

A condition describing LP maximization problems having solutions that can become infinitely large without violating any stated constraints.

The row containing the figures for gross profit or loss given up by adding one unit of a variable into the solution.