Question 1

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that
A) an alternate optimal solution exists.
B) an error in formulation has been made.
C) the right hand sides should be increased.
D) the objective function needs new coefficients.

Accepted Answer

An alternate optimal solution exists when a variable is at its bound (either lower or upper) and has a reduced cost of zero, indicating that moving away from this bound does not improve or worsen the objective value, hence multiple optimal solutions are possible.

Question 2

Analytic Solver Platform provides all of the following reports except
A) Answer
B) Sensitivity
C) Cost performance
D) Limits

Accepted Answer

Analytic Solver Platform provides various reports for optimization and simulation models, including Answer, Sensitivity, and Limits reports. However, it does not specifically provide a report named "Cost performance," which is more of a concept or metric used in project management and cost accounting rather than a report generated by optimization or simulation software.

Question 3

A manager should consider how sensitive the model is to changes in all of the following except
A) differential coefficients.
B) objective function coefficients.
C) constraint coefficients.
D) right-hand side values for constraints.

Accepted Answer

The sensitivity of the model to changes in differential coefficients is not relevant as it is not a parameter in linear programming models. The sensitivity analysis in linear programming models focuses on the changes in objective function coefficients, constraint coefficients, and right-hand side values for constraints.

Question 4

A solution to the system of equations using a set of basic variables is called
A) a feasible solution.
B) basic feasible solution.
C) a nonbasic solution.
D) a nonbasic feasible solution

Accepted Answer

A basic feasible solution is a solution where a set of basic variables are chosen and all other variables are set to 0. This solution is not only feasible (meaning it satisfies all constraints), but also satisfies the condition of having linearly independent constraint equations. A nonbasic solution is one where not all basic variables are chosen, while a nonbasic feasible solution does not satisfy the condition of having linearly independent constraint equations.

Question 5

The simplex method of linear programming (LP):
A) moves to better and better corner point solution of the feasible region until no further objective function improvement can be achieved
B) explicitly enumerates all corner points of the feasible region and selects the best objective function value
C) evaluates all constraints for feasibility
D) does not covert all constraints to equalities

Accepted Answer

The simplex method starts from an initial corner point solution and moves to better and better corner point solutions until no further improvement can be made. It does not explicitly enumerate all corner points or evaluate all constraints for feasibility. The method also converts all constraints to equalities through the introduction of slack or surplus variables.

Question 6

What is the value of the objective function if X₁ is set to 0 in the following Limits Report? A) 80 B) 800 C) 2400 D) 3200

Accepted Answer

The answer of What is the value of the objective...

Question 7

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁ + X₂ + S₁ = 100 A) 0 B) 50 C) 100 D) can't be determined from the given information

Accepted Answer

Since X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds, they are both 0. Therefore, the slack variable S₁ must take on the value of 100 to satisfy the equation.

Question 8

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the
A) Status report
B) Slack report
C) Answer report
D) Cell Value report

Accepted Answer

The Answer report in optimization problems provides information on the slack or surplus for each constraint, indicating the difference between the RHS and the LHS values at the optimal solution.

Question 9

The coefficients in an LP model (c_j, a_ij, b_j) represent A) random variables. B) numeric constants. C) random constants. D) numeric variables.

Accepted Answer

The coefficients in an LP model are numeric constants that represent the values of the decision variables, constraints, and objective function coefficients. They are not random variables or random constants, and their values are determined by the problem formulation. Therefore, B is the best choice.

Question 10

Binding constraints have
A) zero slack.
B) negative slack.
C) positive slack.
D) surplus resources.

Accepted Answer

Binding constraints are those constraints that limit the feasible region of the problem, and they have zero slack (i.e., no unused resources). This means that if the value of the decision variable increases, the value of the objective function does not increase, as the constraint is already fully utilized. Therefore, the correct answer is A (zero slack).

Question 11

The allowable increase for a changing cell (decision variable) is
A) how many more units to produce to maximize profits.
B) the amount by which the objective function coefficient can increase without changing the optimal solution.
C) how much to charge to get the optimal solution.
D) the amount by which constraint coefficient can increase without changing the optimal solution.

Accepted Answer

The allowable increase for a changing cell (decision variable) refers to the amount by which the objective function coefficient can increase without changing the optimal solution, not the production units, pricing strategy, or constraint coefficient.

Question 12

The absolute value of the shadow price indicates the amount by which the objective function will be
A) improved if the corresponding constraint is loosened.
B) improved if the corresponding constraint is tightened.
C) made worse if the corresponding constraint is loosened.
D) improved if the corresponding constraint is unchanged.

Accepted Answer

The absolute value of the shadow price indicates the amount by which the objective function will be improved if the corresponding constraint is loosened. Therefore, option A is the correct answer.

Question 13

If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?
A) increase of 100
B) increase of 110
C) decrease of 100
D) increases but by unknown amount

Accepted Answer

Adding 110 units of the resource may or may not result in an increase of the objective function value. The allowable increase of 100 units is the maximum increase that can be made to the constraint without changing the optimal solution. Any increase beyond that may require a change in the optimal solution, and therefore the increase in the objective function value is unknown without further analysis.

Question 14

What needs to be done to the two constraints in order to convert the problem to a standard form? 
A) a slack variable needs to be added to each constraint to convert them to equalities.
B) nothing.
C) they need to be combined to a single constraint.
D) they need to be subtracted side-by-side

Accepted Answer

To convert the problem to a standard form, we need to have all constraints as equalities. Thus, we need to add slack variables to each constraint.

Question 15

A spider plot
A) is a graphical representation of multiple optimization runs
B) requires multiple runs of the problem
C) is computationally expensive to generate for problems with many constraints and variables
D) all of the above

Accepted Answer

A spider plot is a graphical representation of multiple optimization runs, which requires multiple runs of the problem. It can also be computationally expensive to generate for problems with many constraints and variables. Therefore, option D is the correct answer.

Question 16

The sensitivity analysis provides information about which of the following?
A) the impact of a change to an objective function coefficient.
B) the impact of a change in a resource level.
C) the impact of adding simple upper or lower bounds on a decision variable.
D) all of these.

Accepted Answer

Sensitivity analysis provides information about the impact of changes to objective function coefficients, resource levels, and simple upper or lower bounds on decision variables. Therefore, option D - all of these - is the correct choice.

Question 17

Finding a robust solution to an LP problem
A) is one of the many useful features of the Analytic Solver Platform
B) is trivial
C) is a guessing procedure
D) all of the above

Accepted Answer

Finding a robust solution to an LP problem is not trivial and not a guessing procedure. The Analytic Solver Platform offers useful features to help solve such problems.

Question 18

The optimization technique that locates solutions in the interior of the feasible region is known as
A) sub-optimal optimization
B) sensitivity analysis
C) robust optimization
D) USET optimization

Accepted Answer

The optimization technique that locates solutions in the interior of the feasible region is known as robust optimization. This technique aims to find a solution that is robust and insensitive to small perturbations in the problem parameters. This means that the solution will remain optimal even if there are slight changes in the constraints or objectives of the problem. Sub-optimal optimization refers to techniques that find solutions that are close to optimal but not necessarily the best. Sensitivity analysis involves examining how changes in the problem parameters affect the optimal solution. USET optimization is not a commonly recognized term in the field of optimization.

Question 19

A binding less than or equal to (≤) constraint in a maximization problem means
A) that all of the resource represented by the constraint is consumed in the solution.
B) it is not a constraint that the level curve contacts.
C) another constraint is limiting the solution.
D) the requirement for the constraint has been exceeded.

Accepted Answer

A binding constraint in a maximization problem means that all of the resource represented by the constraint is consumed in the optimal solution, indicating that the constraint is active and limits the solution.

Question 20

A change in the right hand side of a constraint changes
A) the slope of the objective function
B) objective function coefficients
C) other right hand sides
D) the feasible region

Accepted Answer

A change in the right hand side of a constraint affects the feasible region by either expanding or contracting it, depending on whether the change increases or decreases the constraint limit. This does not affect the slope of the objective function, the objective function coefficients, or other right hand sides directly.

Quiz 4: Sensitivity Analysis and the Simplex Method

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Analytic Solver Platform provides all of the following reports except

A manager should consider how sensitive the model is to changes in all of the following except

A solution to the system of equations using a set of basic variables is called

The simplex method of linear programming (LP) :

What is the value of the objective function if X₁ is set to 0 in the following Limits Report?

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁ + X₂ + S₁ = 100

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the

The coefficients in an LP model (c_j, a_ij, b_j) represent

Binding constraints have

The allowable increase for a changing cell (decision variable) is

The absolute value of the shadow price indicates the amount by which the objective function will be

If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?

What needs to be done to the two constraints in order to convert the problem to a standard form?

A spider plot

The sensitivity analysis provides information about which of the following?

Finding a robust solution to an LP problem

The optimization technique that locates solutions in the interior of the feasible region is known as

A binding less than or equal to (≤) constraint in a maximization problem means

A change in the right hand side of a constraint changes