Chapter 2

The case in which more than one solution provide the optimal value for the objective function.

An equation or inequality that rules out certain combinations of decision variables as feasible solutions.

A controllable input for a linear programming model.

are the feasible solution points occurring at the vertices or “corners” of the feasible region. With two-variable problems, these are determined by the intersection of the constraint lines.

The set of all feasible solutions.

solution that satisfies all the constraints.

The situation in which no solution to the linear programming problem satisfies all the constraints.

Mathematical expressions in which the variables appear in separate terms and are raised to the first power.

Another term for linear programming model. Linear programming model A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables.

A representation of a problem where the objective and all constraint conditions are described by this.

A constraint that does not affect the feasible region. If a constraint is redundant, it can be removed from the problem without affecting the feasible region.

A set of constraints that requires all variables to be nonnegative.

The process of translating the verbal statement of a problem into a mathematical statement called the mathematical model.

A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resource.

A variable subtracted from the left-hand side of a greater-than-or equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level.

A linear program in which all the constraints are written as equalities. The optimal solution of this of a linear program is the same as the optimal solution of the original formulation of the linear program.

If the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints, the problem is said to be ….