Optimization Exam 1

Question 1

Any specification of the decision variables that satisfies all of the model’s constraints.

Answer 1

Feasible Region

Question 2

The amounts of things that will minimize or maximize something.

Answer 2

Decision Variables

Question 3

Any point in the feasible region.

Answer 3

Feasible Point

Question 4

Any point in the feasible region that optimizes the objective function.

Answer 4

Optimal Solution

Question 5

The objective function evaluated at the optimal solution.

Answer 5

Optimal Value

Question 6

A line on which all points have the same z-value in a max problem.

Answer 6

Isoprofit Line

Question 7

A line on which all points have the same z-value in a min problem.

Answer 7

Isocost Line

Question 8

If the left hand side and right hand side of the constraint are equal when the optimal values of the decision variables are substituted into the constraint.

Answer 8

Binding Constraint

Question 9

If the left hand side and right hand side of the constraint are unequal when the optimal values of the decision variables are substituted into the constraint.

Answer 9

Nonbinding Constraint

Question 10

For a set of points S, if the line segment joining any pair of points is wholly contained in S.

Answer 10

Convex Set

Question 11

If each line segment that lies completely in a convex set S and contains the point P has a P as an endpoint of the line segment.

Answer 11

Extreme Point

Question 12

The feasible region of a problem contains points for which the value of at least one variable can assume arbitrary large values.

Answer 12

Unbounded Feasible Region

Question 13

No possible point that satisfies the constraints.

Answer 13

Infeasible LP

Question 14

Transforms a given matrix A into a new matrix A’.

Answer 14

Elementary Row Operation (ERO)

Question 15

An algorithm that can be used to solve systems of linear equations.

Answer 15

Gauss-Jordan Elimination

Question 16

A variable that appears with a coefficient of 1 in a single equation and a coefficient of 0 in all other equations.

Answer 16

Basic Variable

Question 17

Any variable that isn’t a basic variable.

Answer 17

Nonbasic Variable

Question 18

An LP that has a maximum objective, non-negative right hand side, only equality constraints, and non-negative decision variables.

Answer 18

Standard Form LP

Question 19

Picks up slack for inequalities.

Answer 19

Slack Variable

Question 20

Any basic solution to the system Ax=b in which all variables are non-negative.

Answer 20

Basic Feasible Solution (BFS)

Question 21

A point in the feasible region of an LP is an extreme point if and only if it is a basic feasible solution to the LP.

Answer 21

Theorem 1

Question 23

If two basic solutions and their sets of basic variables have m-1 basic variables in common. m = number of constraints.

Answer 23

Adjacent Basic Variables