IEOPER Quiz 2 Flashcards
Are all feasible regions considered to be convex sets?
Yes
Graphical method is applicable for __________ variables
2-3
True or False. An LP may have a feasible solution even though an artificial appears at a positive level in the optimal iteration
False
True or False. In an LP with m constraints, a simplex iteration may include more than m positive basic variables.
False
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.
False
True or False. In the simplex method, the feasibility conditions for the maximization and minimization problems are different.
False
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.
False
True or False. The simplex method may not move to an adjacent extreme point if the current iteration is degenerate.
True
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.
False
True or False. The intersection of any two constraints is an extreme point, which is a corner of the feasible region.
False
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.
True
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.
True
If an artificial variable is positive in the optimal simplex tableau, the original problem is ________.
Infeasible
When more than one solution best meets the objective of a linear programming problem, it is said to have ______.
Multiple Optimal Solutions
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 _____.
Unbounded
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.
Cycling
Any two isoprofit or isocost lines for a given linear programming problem are ______ to each other.
Parallel
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 _________.
Redundant
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.
Artificial
The current value of the objective function for any simplex tableau is found in the _______ row and the _______ column.
Z, Solution
In the simplex method, if we choose the wrong EV, we would expect __________.
To have longer iterations
In the simplex method, if we choose the wrong LV, we would expect __________.
The next iteration would be infeasible.
In converting a constraint to standard form, if the constraint presented shows a greater than or equal to symbol, you must add a ___________.
Surplus Variable; - Sn
In converting a constraint to standard form, if the constraint presented shows a less than or equal to symbol, you must add a ___________.
Slack Variable ; + Sn
In converting a constraint to standard form, if the constraint presented shows an equal symbol, you must add a ___________.
None. You must keep it as is since it is already in standard format.
In addition to adding surplus variables or no variables to constraints with >= or + signs, you must also add ____________.
Artificial variables, represented by Rn
Adding artificial variables allows us to use the ______ as our initial solution and meet the requirements of the ____________.
origin, simplex tableau
For the big M technique, you have to ________ the summation of MRi to the untransposed minimization problem
Add
For the big M technique, you have to ________ the summation of MRi to the untransposed maximization problem
Subtract
In Two Phase Technique, the objective function of phase 1 must always be ____________. wherein ____________.
Minimization, Min R0 = R1 + R2
In the tableau, when getting the ratio, it must always be a _______ value.
Positive
Inputs in the tableau must be in __________ form.
Standard
In representing LP models in matrix form, the objective function is given as ______.
Max z = CX
wherein C = Objective function coefficient vector (row)
X = Variable vector (column)
In representing LP models in matrix form, the constraint is given as ______.
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)
In representing LP models in matrix form, the non-negativity constraint is given as ______.
Null vector (column)
A solution that satisfies all of the constraints
Feasible solution
A solution that violates at least one constraint
Infeasible solution
Set of all feasible solutions
Feasible Region / Solution Space
Intersection of 2 or more constraints
Corner Point / Extreme Point
Constraints that do not have any effect on the feasible region
Redundant constraints
Constraints that are satisfied fully at optimum
Binding constraints
n
Number of variables in the LP model (standard form)
m
Number of constraints in the LP model
A solution obtained when all (n-m) variables are equated or assumed to be zero
Basic Solution
A basic solution where all values of the remaining m variables are non-negative
Feasible Basic solution
A region is __________ if for any 2 points on the set, the line joining the 2 points will always lie entirely within the region
Convex
If a negative value is present in the solution column of the tableau, it might be a/an ____________.
Infeasible solution
An NBV with a zero coefficient in the Z-row indicates ________.
Multiple Optimal Solutions
