IEOPER Quiz 2

Question 1

Are all feasible regions considered to be convex sets?

Answer 1

Yes

Question 2

Graphical method is applicable for __________ variables

Answer 2

2-3

Question 3

True or False. An LP may have a feasible solution even though an artificial appears at a positive level in the optimal iteration

Answer 3

False

Question 4

True or False. In an LP with m constraints, a simplex iteration may include more than m positive basic variables.

Answer 4

False

Question 5

True or False. The selection of the entering variable from among the current non-basic variables as the one with the most negative objective coefficient guarantees the most increase in the objective value in the next iteration.

Answer 5

False

Question 6

True or False. In the simplex method, the feasibility conditions for the maximization and minimization problems are different.

Answer 6

False

Question 7

True or False. If the basic feasible solution obtained at the current iteration is degenerate, then the objective function value remains unchanged in the next iteration.

Answer 7

False

Question 8

True or False. The simplex method may not move to an adjacent extreme point if the current iteration is degenerate.

Answer 8

True

Question 9

True or False. In the simplex method, optimality is signaled by the presence of all negative values in the Cj - Zj row in a minimization problem and all positive values in that row for a maximization problem.

Answer 9

False

Question 10

True or False. The intersection of any two constraints is an extreme point, which is a corner of the feasible region.

Answer 10

False

Question 11

True or False. If the leaving variable does not correspond to the minimum ratio, at least one basic variable will definitely become negative in the next iteration.

Answer 11

True

Question 12

True or False. Given the three extreme points A, B, and C of an LP, if A is adjacent to B and B is adjacent to C, then A can be determined from C by interchanging exactly two basic and two non-basic variables.

Answer 12

True

Question 13

If an artificial variable is positive in the optimal simplex tableau, the original problem is ________.

Answer 13

Infeasible

Question 14

When more than one solution best meets the objective of a linear programming problem, it is said to have ______.

Answer 14

Multiple Optimal Solutions

Question 15

When using the least non-negative quotient rule to find the row to be replaced, we might find all such quotients to be negative. If so, the solution is _____.

Answer 15

Unbounded

Question 16

If the value of a basic variable in the solution is zero, the solution is degenerate. In such instance, _________ of the simplex algorithm may result if successive pivots do not produce an improvement in the objective value of the problem.

Answer 16

Cycling

Question 17

Any two isoprofit or isocost lines for a given linear programming problem are ______ to each other.

Answer 17

Parallel

Question 18

If there exists a constraint that lies completely outside the feasible region as determined by the other constraints in the problem, we say that this constraint is _________.

Answer 18

Redundant

Question 19

If there are equality constraints or greater-than-or-equal-to constraints, it is necessary to add a(n) ______ variable to each such constraint to find an initial solution for the simplex method. In a maximization problem, these variables are assigned arbitrarily ______ cost coefficients in the objective function.

Answer 19

Artificial

Question 20

The current value of the objective function for any simplex tableau is found in the _______ row and the _______ column.

Answer 20

Z, Solution

Question 21

In the simplex method, if we choose the wrong EV, we would expect __________.

Answer 21

To have longer iterations

Question 22

In the simplex method, if we choose the wrong LV, we would expect __________.

Answer 22

The next iteration would be infeasible.

Question 23

In converting a constraint to standard form, if the constraint presented shows a greater than or equal to symbol, you must add a ___________.

Answer 23

Surplus Variable; - Sn

Question 24

In converting a constraint to standard form, if the constraint presented shows a less than or equal to symbol, you must add a ___________.

Answer 24

Slack Variable ; + Sn

Question 25

In converting a constraint to standard form, if the constraint presented shows an equal symbol, you must add a ___________.

Answer 25

None. You must keep it as is since it is already in standard format.

Question 26

In addition to adding surplus variables or no variables to constraints with >= or + signs, you must also add ____________.

Answer 26

Artificial variables, represented by Rn

Question 27

Adding artificial variables allows us to use the ______ as our initial solution and meet the requirements of the ____________.

Answer 27

origin, simplex tableau

Question 28

For the big M technique, you have to ________ the summation of MRi to the untransposed minimization problem

Answer 28

Add

Question 29

For the big M technique, you have to ________ the summation of MRi to the untransposed maximization problem

Answer 29

Subtract

Question 30

In Two Phase Technique, the objective function of phase 1 must always be ____________.

Answer 30

Minimization