IEOPER1 Quiz 2 Flashcards
If all the constraints are >= inequalities in a linear programming problem whose objective function is to be maximized (assume that all coefficients
in the linear programs’ constraints and objective function are greater than zero.), then
A. One of the constraints is redundant
B. None of the above
C. The problem is infeasible
D. The solution is unbounded and the objective function value is infinite
B. None of the above
Multiple optimal solutions can occur when the objective function is _________ to a constraint line
Parallel
A slack variable is _________________________
The amount by which the left side of a <= constraint is smaller than the right side
For a maximization problem, we would never pick a column with a positive coefficient in the Z-row as our pivot column because:
A. All of the above
B. It could cause the simplex algorithm to cycle
C. It could cause the objective value to decrease in the next solution
D. It could result in an infeasible solution
C. It could cause the objective function value to decrease in the next solution.
True or False. In an LP model, the feasible solution space can be changed when non-binding constraints are deleted
True
True or False. In an LP model, the feasible solution space can be affected when redundant constraints are deleted.
False; removing redundant constraints does not change the set of possible solutions.
True or False. In an LP model, the variable representing the activity with the largest profit per unit in the objective function will always appear at a positive level in the optimal solution.
False; it would depend on the constraints and how they interact.
True or False. An artificial variable column can be dropped altogether from the simplex tableau once the variable becomes non-basic.
True
If an isoprofit line yielding the optimal profit lies directly on a constraint line rather than a point on one or more constraints, then:
A. The solution is infeasible
B. The solution is unbounded
C. None of the above
D. One of the constraints is redundant
C. None of the above; it indicates that there are multiple optimal solutions
The ______ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant.
Certainty
A possible decrease in the cost of a minimization problem is indicated by _____________
A negative value of the coefficient of a surplus variable in the Z-row
The problem caused by a redundant constraint through a feasible corner point is that _______________.
It may waste simplex iterations by cycling in just one and the same corner point.
The selection of the leaving variable as the variable with the minimum non-negative ratio between the right-hand side value and the corresponding pivot column guarantees that:
A. None of the above
B. No constraint is violated
C. The next iteration is a feasible solution
D. The solution moves to an adjacent feasible corner point
E. All of the above
E. All of the above
A variable which is not included in the basic column of a particular simplex tableau is:
A. always equal to zero
B. called a slack or surplus variable
C. called a non-basic variable
D. both a and c
E. none of the above
D. Both A and C
If a problem has one >= and one <= constraint and the two do not intersect in the quadrant of the graph where both variables are positive. (assume that all coefficients in the linear programs’ constraints and objective function are greater than zero):
A. The problem is infeasible
B. None of the above
C. The solution is unbounded
D. One of the constraints is redundant
A. The problem is infeasible
Which of the following statements is not true?
A. An optimal solution satisfies all constraints
B. A feasible solution point does not have to lie on the boundary of the feasible solution
C. A feasible solution satisfies all constraints
D. An infeasible solution violates all constraints
D. An infeasible solution violates all constraints
In a maximization problem using the Big M Technique, artificial variables are multiplied with a very large negative number and are then added to the objective function to ______________________.
Encourage the model to zero out the values of the artificial variables
True or False then state the reason. Artificial variables serve as artificial slack variables that create an artificial origin as a starting solution in solving all LP models.
True (But was marked wrong in OT)
If a basic variable is equal to zero, then it is __________
Degenerate
Indicator/s for No Feasible Solution:
Optimal tableau contains an artificial variable as the basic variable
If the LP model results in an infeasible solution situation, it implies that __________________.
The demands of the system could not be met simultaneously
What could be a possible solution to the special case of “No feasible solution”?
Adjust the capacity/demand constraint
Multiple optimal solutions imply that ________________.
There are other solutions that yield the same maximum or minimum value of Z.
Indicator/s for Multiple Optimal Solution:
In graphical method, the objective function is parallel to a binding constraint
In the optimal tableau, the coefficient of an NBV is 0 and there is an LV if you make the said NBV an EV.
Define binding constraint
Substituting variables (X1, X2, etc) will make the LHS = RHS. These are constraints that intersect to form the optimal point.
If the LP model results in a multiple optimal solutions situation, it implies that __________________.
Management is given flexibility in implementing the more beneficial solution
Indicator/s for Unbounded Solution Space (Infinite and Finite):
Constraint coefficients of an NBV in the tableau are non-positive (0 and negative numbers) at any iteration
If the NBV is also qualified to be an EV, it would have an infinite z value (Stop iterations).
If the NBV does not qualify as an EV, then it would have a finite z value (proceed with iterations).
Unbounded solution space implies that ____________.
One or more non-redundant constraints have not been accounted for in the constraints
Inaccurate estimate of parameters
Indicator/s for Degeneracy:
One or more BVs are equal to 0. This happens when, in the previous iteration, there are at least 2 variables that are tied for the minimum ratio when selecting the LV.
Graphically, it would be shown as an over-determined corner point
Degeneracy implies that __________.
There is at least one redundant constraint in the LP model
If the optimal solution occurs at the over-determined corner point, then we would have _______________.
Permanent degeneracy
In the simplex iterations, the indicator of a degenerate solution will happen ___________________________.
A corner point before the degenerate corner point. (iteration before)
An over-determined feasible corner point means that ___________________.
At least 3 lines or constraints intersect to form a corner point.
In a degenerate solution tableau, if the chosen leaving variable has a solution value of 0, then that would be an indicator of _______________.
Permanent degeneracy
In a degenerate solution tableau, if the chosen leaving variable has a positive solution value other than 0, then that would be an indicator of _______________.
Temporary degeneracy
True or False then state the reason. The number of basic variables is always equal to the number of functional constraints in any iteration
True
True or False then state the reason. The minimum ratio in a simplex iteration corresponds to the value in the next iteration of the chosen entering variable
True
True or False then state the reason. In the simplex algorithm, choosing the basic variable that has the smallest non-negative ratio (ratio of the solution column value to the coefficient in the pivot column) as the leaving variable ensures that the next iteration will be feasible.
True
True or False then state the reason. In the simplex algorithm, choosing the basic variable that has a zero ratio (ratio of solution column value to the coefficient in the pivot column) as the leaving variable will make the next iteration reveal multiple optimal solutions.
False; it would reveal a degenerate solution
True or False then state the reason. If the slack variable associated with a resource constraint is basic at optimum, it will be beneficial for the company to consider increasing the value of that particular resource.
False. The basic variables have to be basic at the optimum
True or False then state the reason. 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, then the only way that D can be determined from A is by interchanging exactly three basic and three non-basic variables
False. Interchange only one BV and one NBV at a time.
True or False then state the reason. In a minimization LP model, the selection of the least positive objective function coefficient as the entering variable will lead to the least decrease in the z-value of the next iteration. This is why the variable which has the most positive objective function coefficient is chosen as the entering variable
False
True or False then state the reason. An LP model with at least one >= or = constraint cannot be solved without adding artificial variables
False
True or False then state the reason. In the simplex method, one iteration corresponds to exactly one feasible corner point and vice-versa.
False. In any method (i think)
True or false then state the reason. If a feasible corner point corresponding to a current simplex iteration is determined by the intersection of five constraints, then there should be three basic variables that tie for the minimum ratio (selection of LV) in the previous simplex iteration.
False. It would be five basic variables if ever there was an intersection of five constraints
True or False. In a maximization LP model, the selection of the most negative objective function coefficient as the entering variable will lead to the greatest increase in the z-value of the next iteration.
False
True or False. In a linear programming problem, introducing a constraint can only increase or maintain the value of the objective function.
False
True or False. If there are several optimal solutions to a linear programming problem, they must all be located at the edge of the feasible region
True
True or False. It is possible to optimize many objective functions at once in linear programming problem
False (based on copilot)
True or False. An infinite number of optimal solutions to a linear programming problem is implied if the feasible region is unbounded.
False (based on copilot)
True or False. If an LP problem has an optimal solution, it will have a solution at some corner (vertex) of the feasible region.
True
True or False. In the simplex method, a basic solution assigns the value zero to all active variables.
False
True or False. Excel Solver which can be used in solving LP problems is found in the formulas tab of MS Excel
False
True or False. No point other than a corner of the feasible region can be a solution to an LP problem
False
True or False. You should always make sure that there are no negative numbers in the rightmost column (with the possible exception of the objective) before choosing a pivot.
True
True or False. Constraints can always be turned into equations by adding or subtracting slack or surplus variables from the left-hand sides as appropriate
True
Interior Point Algorithm was made by ____________.
Narendra Karmarkar
