IEOPER1 Finals Review

Question 1

What are the four inherent assumptions in formulating LP models?

Answer 1

Proportionality
Additivity
Divisibility
Certainty

Question 2

What was the name of the first group of experts tasked to perform research on military operation problems, specifically the effectiveness of use of military weapons?

Answer 2

Blackett’s Circus

Question 3

What are the two types of mathematical models?

Answer 3

Deterministic
Stochastic

Question 4

During the 1950s, TIMS was founded. What does TIMS stand for?

Answer 4

The Institute of Management Science

Question 5

Who developed the simplex algorithm?

Answer 5

George Dantzig

Question 6

In what year was the simplex algorithm developed?

Answer 6

1947

Question 7

True or False. The condition of [multiple optimal solutions] may only be determined in the last or optimal iteration of the simplex method

Answer 7

True

Question 8

True or False. In the simplex algorithm, choosing the basic variable that has the smallest non-negative ratio (ratio of the solution column to the coefficient in the pivot column) as the leaving variable ensures that the next iteration will be [feasible]

Answer 8

True

Question 9

True or False. If the objective function line is not parallel to any functional constraint, it is still [possible to have multiple optimal solutions]

Answer 9

True

Question 10

True or False. Permanent degeneracy means that [the optimal solution occurs at an overdetermined corner point]

Answer 10

True

Question 11

True or False. Given the four feasible corner points, A, B, C, and D of an LP model, if A is adjacent to B, B is adjacent to C, C is adjacent to D and D is adjacent to A, and corner point C corresponds to the optimal solution, [then corner point D can only be determined from A by interchanging exactly one basic and one non-basic variable.]

Answer 11

True

Question 12

True or False. Temporary degeneracy means that a redundant constraint intersects a [non-optimal feasible corner point]

Answer 12

True

Question 13

True or False. In the simplex method, [one feasible corner point may correspond to two iterations.]

Answer 13

True

Question 14

True or False. If two constraints intersect at the optimal point, [then the slack/surplus variables associated with the two constraints must be non-basic]

Answer 14

True

Question 15

True or False. Under degenerate conditions, the number of feasible basic solutions is [definitely larger] than the number of feasible corner points.

Answer 15

True

Question 16

True or False. In a simplex iteration, if there is an entering variable but no leaving variable can be chosen, then it means that the LP model has [no feasible solution]

Answer 16

False. Unbounded (copilot)

Question 17

True or False. If three variables in a simplex iteration tie for the minimum ratio in choosing the leaving variable, then it means that the simplex procedure moves to a feasible corner point which is intersected by [three redundant constraints]

Answer 17

False. Three non-redundant constraints

Question 18

True or False. In the simplex algorithm, choosing the basic variable that has a zero ratio (ratio of a solution column value to the coefficient in the pivot column) as the leaving variable will make the next iteration reveal [multiple optimal solutions]

Answer 18

False. Permanent degenerate optimal solution

Question 19

True or False. An LP model with at least one >= or = constraint [cannot be solved] without adding artificial variables

Answer 19

False. It can be solved using other methods

Question 20

True or False. If an LP model has an unbounded solution space, it means that there may be a [redundant constraint] in the model

Answer 20

False. Non-redundant constraints that have not been accounted for

Question 21

True or False. If the objective function is not parallel to any [functional constraint], then it is therefore not possible to have multiple optimal solutions

Answer 21

False.