Optimization Final Exam

Question 1

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

Answer 1

Feasible Region

Question 2

Any point in the feasible region.

Answer 2

Feasible Point

Question 3

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

Answer 3

Isoprofit Line

Question 4

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

Answer 4

Isocost Line

Question 5

If the LHS and RHS of a constraint are equal when the optimal values of the decision variables are substituted into the constraint.

Answer 5

Binding Constraint

Question 6

If the LHS and RHS of a constraint are unequal when the optimal values of the decision variables are substituted into the constraint.

Answer 6

Nonbinding Constraint

Question 7

If the line segment joining any pair of points in S is wholly contained in S.

Answer 7

Convex Set

Question 8

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

Answer 8

Extreme Point

Question 9

There are points in the feasible region with arbitrarily large z - values.

Answer 9

Unbounded LP

Question 10

The feasible region contains no points.

Answer 10

Infeasible LP

Question 11

Two or more extreme points are optimal, and the LP will have an infinite number of optimal solutions.

Answer 11

Multiple Optimal Solutions

Question 12

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

Answer 12

Basic Variable

Question 13

Any solution to the system Ax=b in which all variables are nonnegative.

Answer 13

Basic Feasible Solution

Question 14

For any LP with m constraints, if its set of basic variables have m-1 basic variables in common.

Answer 14

Adjacent Basic Solutions

Question 15

If there is no nonbasic variables with a zero coefficient in row 0 of the optimal tableau.

Answer 15

Unique Solution

Question 16

In an optimal tableau, there exists a NBV with coefficient zero in row 0, and continuing the Simplex algorithm will obtain another optimal tableau with a different solution.

Answer 16

Alternative Optimal Solution

Question 17

When a variable with a negative coefficient in row 0 has a nonpositive coefficient in each constraint.

Answer 17

Unbounded LP

Question 18

If an LP has at least one BFS in which a basic variable is equal to zero.

Answer 18

Degenerate LP

Question 19

The artificial variable remains positive in the final tableau.

Answer 19

Infeasible LP

Question 20

Let x = [x1, x2, … xn] be any feasible solution to the primal and y = [y1, y2, … yn] be any feasible solution to the dual. Then (z-value for x) <= (w-value for y).

Answer 20

Weak Duality

Question 21

If the primal LP has an optimal solution, then its dual also has an optimal solution, and the optimal values of their objective functions are equal.

Answer 21

Strong Duality

Question 22

Unbounded Primal

Answer 22

Dual Infeasible

Question 23

Unbounded Dual

Answer 23

Primal Infeasible

Question 24

If the primal has an optimal solution, then the dual has an optimal solution. Also z = w.

Answer 24

The Dual Theorem

Question 25

The amount by which the optimal z-value is improved if we increase bi by 1.

Answer 25

Shadow Price

Question 26

What’s true about shadow price?

Answer 26

The shadow price of the ith constraint of a max problem = the optimal value of the ith dual variable.

Question 27

Ensures that the total quality produced does not exceed plant capacity.

Answer 27

Supply Constraint

Question 28

Ensures that a location receives its demand.

Answer 28

Demand Constraint

Question 29

The LP obtained by omitting all integer or 0-1 constraints on variables.

Answer 29

LP Relaxation