Question 1

The ________________________ for a constraint is the amount the optimal objective value will change if the right-hand-side of the constraint is increased by one unit.
A) Changing Price
B) Opportunity Cost
C) Shadow Price
D) Opportunity Price
E) Shadow Cost

Accepted Answer

The term "shadow price" refers to the value of a resource in a linear programming problem. It represents the amount by which the value of the objective function would increase or decrease for each unit increase or decrease in the availability of the resource. Therefore, the shadow price is the answer to the given question.

Question 2

A feasible solution to an optimization problem is a particular combination of decision variables that satisfies some of the constraints.

Accepted Answer

A feasible solution to an optimization problem is a particular combination of decision variables that satisfies all of the constraints, not just some of them.

Question 3

Constraints that are not at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value not equal to the right-hand-side value, are called _________________________.
A) inequality constraints
B) non-binding constraints
C) binding constraints
D) limiting constraints
E) shadow constraints

Accepted Answer

Non-binding constraints are the constraints that are not at their limits at the optimal solution of a linear program. Their left-hand-side value is less than the right-hand-side value, indicating that they do not play an active role in determining the solution. In contrast, binding constraints are at their limits and determine the feasibility of the solution. Therefore, option B is the correct answer.

Question 4

The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include:
A) base value, original value
B) original value, final value
C) base value, final value
D) original value, test value
E) bounded value, un-bounded value

Accepted Answer

The Answer Report in optimization problems typically includes the original value and the final value for the target cell, adjustable cell, and constraints.

Question 5

The algebraic formulation of an optimization problem states the decision variables, objective function, and constraints in algebraic form.

Accepted Answer

The algebraic formulation of an optimization problem involves representing the decision variables, objective function, and constraints in algebraic form.

Question 6

In Linear Programming, users have control over quantities called parameters.

Accepted Answer

In Linear Programming, the quantities that users have control over are called variables, not parameters. Parameters are typically fixed values that define the constraints and objective function.

Question 7

The advantage of formal optimization modeling is that it can simultaneously consider the effects of alternate decisions to produce the best overall decision according to the objective.

Accepted Answer

Formal optimization modeling allows considering different decision alternatives and their consequences to determine the best course of action according to a specific objective or goal. By modeling the problem mathematically and using optimization techniques, it becomes possible to identify the optimal solution that maximizes benefits, minimizes costs or risk, or achieves a balance between conflicting objectives. This approach allows decision-makers to evaluate different scenarios and make more informed and objective decisions based on the available data and assumptions. Therefore, the statement is true that formal optimization modeling can simultaneously consider the effects of alternate decisions to produce the best overall decision according to the objective.

Question 8

To retain model flexibility while using Solver you must:
A) use appropriate color codes
B) enter specific values
C) ensure the inputs and outputs are separated
D) use only cell references
E) use Slack

Accepted Answer

Using only cell references allows for model flexibility as changes to input values will automatically update the output values, without the need to edit specific values or recalculate formulas.

Question 9

The constraints in an optimization model must all be of one type, for example, all ≤, all ≥, or all =.

Accepted Answer

Optimzation models can have multiple types of constraints, including ≤, ≥, =, and even non-linear constraints. The key is to ensure that all constraints are consistent and appropriate for the problem being modeled.

Question 10

All mathematical programs should include non-negativity constraints.

Accepted Answer

Non-negativity constraints are specific to the context of the problem being modeled. Not all mathematical programs require variables to be non-negative; it depends on the nature of the variables and the problem domain.

Question 11

What do you need to do before using Solver?
A) take an Excel class
B) enter solver settings into Excel
C) define all constraints
D) enter Solver options
E) have a working, flexible spreadsheet model

Accepted Answer

Before using Solver, you need to have a working, flexible spreadsheet model. While taking an Excel class and entering Solver options and settings may be helpful, defining all constraints is necessary but not sufficient for using Solver effectively.

Question 12

Strict inequalities (<, >) are not used in optimization problems.

Accepted Answer

Strict inequalities can make it difficult to find feasible solutions, so optimization problems typically use non-strict inequalities (<=, >=) instead.

Question 13

Given a Linear Program with a minimization objective, the optimal objective function value may decrease if a ≥ constraint is added to the program.

Accepted Answer

Adding a ≥ (greater than or equal to) constraint to a minimization Linear Program restricts the feasible region, potentially increasing the minimum value or leaving it unchanged, but it cannot decrease the optimal objective function value.

Question 14

Not-equals-to constraints (≠) are allowable in optimization problems.

Accepted Answer

The answer of Not-equals-to constraints (≠) are allowable in optimization...

Question 15

At the optimal solution of a Linear Program, the difference between the right-hand-side value and the left-hand-side value of a constraint is the ____________________.
A) shadow
B) difference
C) shortfall
D) slack
E) cushion

Accepted Answer

The difference between the right-hand-side value and the left-hand-side value of a constraint at the optimal solution is known as the slack. Slack represents the amount by which the constraint is not fully utilized in the optimal solution. The other options do not accurately describe this concept in linear programming.

Question 16

One use of the Answer report is:
A) to develop the final answer.
B) to duplicate the output results in a new form.
C) as a debugging tool.
D) as a duplication tool.
E) as a results summary printout.

Accepted Answer

The Answer report is used as a debugging tool to help understand and troubleshoot the results of a model or analysis, providing insights into how the final answers were derived.

Question 17

Three reports are available when Solver has successfully found an optimal solution. These are _______.
A) Answer Report, Sensitivity Report, and Limits Report
B) Answer Report, Sensitivity Report, and Constraints Report
C) Answer Report, Limits Report, and Constraints Report
D) Solution Report, Sensitivity Report, and Limits Report
E) Solution Report, Sensitivity Report, and Constraints Report

Accepted Answer

The three reports available when Solver finds an optimal solution are the Answer Report, Sensitivity Report, and Limits Report.

Question 18

An optimal solution to an optimization problem is always feasible.

Accepted Answer

An optimal solution is a feasible solution that optimizes the objective function. Therefore, it must always be feasible. If an optimal solution was not feasible, it would not be considered as a solution to the optimization problem.

Question 19

The optimal solution to an optimization problem is the feasible solution with the largest (for a "min" problem) objective function value.

Accepted Answer

The optimal solution to an optimization problem is the feasible solution with the smallest (for a "min" problem) or largest (for a "max" problem) objective function value, depending on the nature of the problem.

Question 20

In Linear Programming (LP) problems, all of the relationships among the variables are linear.

Accepted Answer

Linear programming problems involve linear relationships among the variables and are solved using linear optimization techniques. Non-linear relationships would require non-linear optimization techniques.

Quiz 18: Introduction to Optimization

The ________________________ for a constraint is the amount the optimal objective value will change if the right-hand-side of the constraint is increased by one unit.

A feasible solution to an optimization problem is a particular combination of decision variables that satisfies some of the constraints.

Constraints that are not at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value not equal to the right-hand-side value, are called _________________________.

The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include:

The algebraic formulation of an optimization problem states the decision variables, objective function, and constraints in algebraic form.

In Linear Programming, users have control over quantities called parameters.

The advantage of formal optimization modeling is that it can simultaneously consider the effects of alternate decisions to produce the best overall decision according to the objective.

To retain model flexibility while using Solver you must:

The constraints in an optimization model must all be of one type, for example, all ≤, all ≥, or all =.

All mathematical programs should include non-negativity constraints.

What do you need to do before using Solver?

Strict inequalities (<, >) are not used in optimization problems.

Given a Linear Program with a minimization objective, the optimal objective function value may decrease if a ≥ constraint is added to the program.

Not-equals-to constraints (≠) are allowable in optimization problems.

At the optimal solution of a Linear Program, the difference between the right-hand-side value and the left-hand-side value of a constraint is the ____________________.

One use of the Answer report is:

Three reports are available when Solver has successfully found an optimal solution. These are _______.

An optimal solution to an optimization problem is always feasible.

The optimal solution to an optimization problem is the feasible solution with the largest (for a "min" problem) objective function value.

In Linear Programming (LP) problems, all of the relationships among the variables are linear.