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Term 3 (2023-2024) > IEOPER Quiz 2 > Flashcards

IEOPER Quiz 2 Flashcards

1
Q

Are all feasible regions considered to be convex sets?

A

Yes

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2
Q

Graphical method is applicable for __________ variables

A

2-3

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3
Q

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

A

False

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4
Q

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

A

False

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5
Q

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.

A

False

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6
Q

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

A

False

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7
Q

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.

A

False

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8
Q

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

A

True

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9
Q

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.

A

False

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10
Q

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

A

False

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11
Q

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.

A

True

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12
Q

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.

A

True

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13
Q

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

A

Infeasible

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14
Q

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

A

Multiple Optimal Solutions

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15
Q

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 _____.

A

Unbounded

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16
Q

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.

A

Cycling

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17
Q

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

A

Parallel

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18
Q

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 _________.

A

Redundant

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19
Q

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.

A

Artificial

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20
Q

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

A

Z, Solution

21
Q

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

A

To have longer iterations

22
Q

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

A

The next iteration would be infeasible.

23
Q

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

A

Surplus Variable; - Sn

24
Q

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

A

Slack Variable ; + Sn

25
Q

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

A

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

26
Q

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

A

Artificial variables, represented by Rn

27
Q

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

A

origin, simplex tableau

28
Q

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

A

Add

29
Q

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

A

Subtract

30
Q

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

A

Minimization, Min R0 = R1 + R2

31
Q

In the tableau, when getting the ratio, it must always be a _______ value.

A

Positive

32
Q

Inputs in the tableau must be in __________ form.

A

Standard

33
Q

In representing LP models in matrix form, the objective function is given as ______.

A

Max z = CX

wherein C = Objective function coefficient vector (row)
X = Variable vector (column)

34
Q

In representing LP models in matrix form, the constraint is given as ______.

A

AX = b

wherein A = Constraint coefficient matrix (m x n)
m = number of functional constraints
n = number of variables

X = variable vector (column)
b = Right-hand side (RHS) vector (column)

35
Q

In representing LP models in matrix form, the non-negativity constraint is given as ______.

A

Null vector (column)

36
Q

A solution that satisfies all of the constraints

A

Feasible solution

37
Q

A solution that violates at least one constraint

A

Infeasible solution

38
Q

Set of all feasible solutions

A

Feasible Region / Solution Space

39
Q

Intersection of 2 or more constraints

A

Corner Point / Extreme Point

40
Q

Constraints that do not have any effect on the feasible region

A

Redundant constraints

41
Q

Constraints that are satisfied fully at optimum

A

Binding constraints

42
Q

n

A

Number of variables in the LP model (standard form)

43
Q

m

A

Number of constraints in the LP model

44
Q

A solution obtained when all (n-m) variables are equated or assumed to be zero

A

Basic Solution

45
Q

A basic solution where all values of the remaining m variables are non-negative

A

Feasible Basic solution

46
Q

A region is __________ if for any 2 points on the set, the line joining the 2 points will always lie entirely within the region

A

Convex

47
Q

If a negative value is present in the solution column of the tableau, it might be a/an ____________.

A

Infeasible solution

48
Q

An NBV with a zero coefficient in the Z-row indicates ________.

A

Multiple Optimal Solutions

Term 3 (2023-2024) (7 decks)

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