Linear Optimization

Question 1

Alternative optimal solutions

Answer 1

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

Question 2

binding constraint

Answer 2

A constraint that holds as an equality at the optimal solution.

Question 3

Constraints

Answer 3

Restrictions that limit the settings of the decision variables.

Question 4

Decision variable

Answer 4

A controllable input for a linear programming model.

Question 5

Extreme point

Answer 5

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

Question 6

Feasible region

Answer 6

the set of all feasible solutions

Question 7

Feasible solution

Answer 7

A solution that satisfies all the constraints simultaneously.

Question 8

Infeasibility

Answer 8

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

Question 9

Linear function

Answer 9

A mathematical function in which each variable appears in a separate term and is raised to the first power.

Question 10

Linear program

Answer 10

A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables.

Question 11

Mathematical Model

Answer 11

A representation of a problem in which the objective and all constraint conditions are described by mathematical expressions.

Question 12

Nonnegativity constraints

Answer 12

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

Question 13

Objective function

Answer 13

The function being maximized or minimized in Linear Programming

Question 14

Objective function coefficient allowable increase (decrease)

Answer 14

The allowable increase/decrease of an objective function coefficient is the amount the coefficient may increase (decrease) without causing any change in the values of the decision variables in the optimal solution. The allowable increase/decrease for the objective function coefficients can be used to calculate the range of optimality.

Question 15

Problem formulation or modeling

Answer 15

process of translating a verbal statement of a problem into a mathematical model

Question 16

Reduced cost

Answer 16

If a variable is at its lower bound of zero, this is equal to the shadow price of the nonnegativity constraint for that variable. In general, if a variable is at its lower or upper bound, this is the shadow price for that simple lower or upper bound constraint.

Question 17

Right-Hand-Side Allowable Increase (Decrease)

Answer 17

The amount the right-hand side may increase (decrease) without causing any change in the shadow price for that constraint. The allowable increase and decrease for the right-hand side can be used to calculate the range of feasibility for that constraint.

Question 18

Sensitivity Analysis

Answer 18

The study of how changes in the input parameters of a linear programming problem affect the optimal solution.

Question 19

Shadow price

Answer 19

The change in the optimal objective function value per unit increase in the right-hand side of a constraint.

Question 20

Slack

Answer 20

The difference between the right-hand-side and the left-hand-side of a less-than-or-equal-to constraint.

Question 21

Slack variable

Answer 21

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 resources.

Question 22

surplus variable

Answer 22

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.

Question 23

Unbounded

Answer 23

The situation in which 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.