MGT 3120 Exam 1

the __________ percent rule for simultaneous changes in constraint right-hand sides is used to determine if a change in two or more right-hand sides will result in the shadow price becoming invalid

100

Which of the following is true?

A cost-trade-off-benefit problem involves minimum goals for the level of benefits; a resource-allocation problem involves limits on the use of a resource

A sensitive parameter is

A parameter which cannot change by even a small amount without leading to a change in the optimal solution

A bakery produces cakes, cookies, and biscuits. The raw materials for these products are all the same ( eggs, flour, water and sugar). The owner of the bakery would like to determine the best mix of products to produce with the materials currently in the bakery. Which of the following are resource constraints for the problem?

Amount of sugar used <= amount of sugar available; amount of flour used <= amount of flour available

In a linear programming model, a solution that satisfies all but one of the constraints is

An infeasible solution

An assignment problem format could be used for which of the following?

Assigning employees to tasks; assigning machines to jobs

the input of managers often leads to model enrichment's in the form of ______ constraints, which allow managers to incorporate additional goals into the model

Benefit

Which of the following is true about the constraints in a linear programming model?

Constraints are used to ensure that the usage of resources does not exceed the supply; constraints are used to ensure that the changing values are nonnegative

In a spreadsheet formulation of a linear programming model, the parameters of the model are

Constraints; shown in the data cells

A linear programming model which attempts to achieve optimal performance while maintaining a minimum level of performance on one or more measures is known as a ________ - _________-trade-off-model

Cost-benefit

In spreadsheet formulation of a linear programming model, the constants shown in the ____ cells are known as the parameters of the model

Data

The first step in building a spreadsheet for a linear programming model is to determine the location of the _______ cells

Data

After finding an optimal solution which maximizes the profitability of a product mix problem, you have been asked to determine how much your solution would change if the availability of a scarce resource decreased by 10%. This can be accomplished in which of the following ways

Decrease the right-hand side of the appropriate resource constraint by 10% and resolve the model

When formulating a linear programming model using the algebraic approach, the first step in the process is to ______ the relevant _____

Gather, Data

The shadow price shows how much the objective function value will __________ if there is a small ____________ in the right-hand side of the constraint

Increase,increase; decrease, decrease

In a linear programming model, the nonnegativity constraints ensure that no decision variable is assigned a value of _____ than zero

Less

In a transportation problem, the activities correspond to the shipping lanes while the ________ of each activity is the quantity shipped

Level

A ______ problem may require an analyst to formulate resource-allocation constraints, fixed-requirement constraints, and benefit constraints in the same model

Mixed

Which of the following statements about linear programming models is false?

Models that can be formulated using algebra cannot be modeled using spreadsheets

In a linear programming model, _______ constraints prevent variables from taking on values of less than zero

Nonnegativity

In a linear programming model, the variable "quantity" is a decision variable. A constraint as "quantity >=" is a

Nonnegativity constraint

In an assignment problem, each task is assigned how many resources?

One

In a linear programming model, the best feasible solution is known as the ______ solution

Optimal

In a spreadsheet, the constraints for a linear programming model are located in the

Output cells

A ________-________ problem requires an analyst to determine how much of the available capacity to allocate to each of a group of products, with the goal of maximizing profits.

Product-mix

In the product-mix problem, data concerning pricing and product is used to estimate

Profit per unit

the goal of ________ optimization is to find a solution for the model that will be feasible and nearly optimal for all plausible combinations of the actual parameter values..

Robust

In a linear programming model, the equation for the output cells can be expressed using which excel functions?

SUMPRODUCT and occasionally SUM

If the right-hand side of a constraint is increased by one unity, the amount that the objective function value will increase is given by the __________ ______________

Shadow price

The allowable range for the right-hand side of a functional constraint shows the range of values for which the __________ ____________ remains valid

Shadow price

In robust optimization, a ___________ constraint is one that can be violated a little bit while a _________ constraint must be satisfied

Soft;hard

If the supply and demand data for a transportation problem involves only integer values, which of the following is true?

There will be an optimal solution that has integer values for all decision variables

Any assignment problem with a feasible solution will have an optimal solution where all changing calls are integers

True

The steps followed in the algebraic approach to linear programming are generally the same as the spreadsheet approach

True

Transportation problem with integer values for the supplies and demands will have an optimal solution that involves shipping only integer quantities

True

__________ - _________ analysis is an important part of a linear programming study, particularly if parameter may be incorrect

What-if

To evaluate the potential impact of a change in the availability of a critical resource, which of the following techniques would be most appropriate?

What-if analysis

If the variable "X" is a decision variable, which of the following is not a functional constraint

X>= 0

in a linear programming model, a solution that satisfies all of the constraints is

a feasible solution

Sensitive analysis is

a form of what-if analysis

Which of the following statements about the changing cells in a linear programming model are true?

a model may have more than one changing cell; each decision will have its own changing cell

to determine the percentage change in two or more objective function coefficients

add the percentage change for each objective function coefficient

which of the following is an assumption of robust optimization with independent parameters?

all functional constraints are in either <= or >= form each parameters value is not influenced by the values of other parameters each parameter has a range of uncertainty

The __________ __________ for an objective function coefficient shows the range of objective function coefficients that will not result in a change on the optimal solution

allowable range

In a linear programming model, the measure of performance is entered as

an equation that calculates performance as the changing cells vary

In a linear programming model, the decision variables ____________ restricted to integer values

are not

Mathematical models utilize simplifying ________ to enable an analyst to build a workable model

assumptions

when a constraint is graphed, the resulting line is called a constraint _____ line

boundary

There will be one _______ cell for each decision to be made in a linear programming model

changing

An objective function line

consists of point which have the same value of the objective function; is parallel to all other objective function lines for the same problem

Using what-if analysis, it is possible to determine the sensitivity of model parameters such as

constraint right-hand side; objective function coefficient

a linear programming model can be formulated in which of the following ways?

diectly on a spreadsheet; as an algebraic model

Model __________ is the addition of features that allow the model to more accurately reflect reality

enrichment

Because the set of feasible solutions is limited, integer programming problems are easier to solve than programming problems

false

For a constraint with an inequality sign, the constraint boundary equation will be the same as that of the constraint itself

false

In analytic solver, each model can have at most one parameter cell

false

in a transportation problem, the amount produced by each source is one of the decisions that has to be determined

false

the graphical method can be used to solve linear programming problems with four decision variables

false

in the graphical method of linear programming, the area where all constraints are satisfied is called the _______ region

feasible

the area of the graph where the optimal solution will be found is called the ______ _______

feasible region

A ________ - _______ constraints is used when the amount provided must be exactly equal to the required amount

fixed-requirement

Transportation problems are a special class of linear programming problems that utilizes only

fixed-requirement constraints

when the certain quantities must achieve specific levels, a linear programming model uses _____ to ensure these goals are met.

fixed-requirement constraints

all the constraints that are not nonegativity are known as _______ constraints

functional

structural constraints are also know as ______ constraints

functional

In analytic solver, chance constraints can be used to allow the original constraints to be treated as a soft constraint but still maintain a ________ probability that the constraint will not be violated

high

In a cost-benefit-trade-off problem, all functional constraints have the form

level achieved>= minimum acceptable level

In analytic solver, the number of different values to display in the parameter analysis report is entered into which field?

major axis points

to identify a robust solution with independent parameters, assign the ______ value for each coefficient on the left of a <= sign of a constraint

maximum

A linear programming problem with both fixed-requirement constraints and resources-allocation constraints is known as a

mixed problem

Which of the following are key categories of linear programming problems?

mixed problems; cost-benefit-trade-off problems; resource-allocation problems

In a spreadsheet, the measure of performance is located in the _______ cell

objective

For a given problem, all the objective function lines are

parallel

In analytical solver, a data cell that contains a parameter which will be systematically varied is known as a ________ cell

parameter

the numbers that go into the data cells of a linear programming model are known as the ______ of the model

parameters

For constraints with inequalities ( for ex <= or >=), the constraint boundary equation is obtained by

replacing the inequality sign with an equality sign

In analytical solver, the dialog box to specify details of parameters cells is found in which menu?

reports

A firm is trying to choose from a set of potential capital projects in a way that maximizes the expected return. The capital budget is limited, so a ______ - _______ model would be appropriate

resource-allocation

Resource-allocation problems are characterized by limits on the usage of ______ while cost-benefit-trade-off problems involve goals concerning the levels of _____.

resources;benefits

the rate of change on the objective function when the right-hand side of a constraint is increased or decreased is known as

shadow price

a _____________ change in a sensitive parameter causes the optimal solution to change

small

In analytic solver, chance constraints can be used to allow the original constraint to be treated as a ___________ constraint but still maintain a high probability that the probability that the constraint will not be violated

soft

A constraint boundary line forms the boundary between _______ that are permitted and those which are not permitted by a particular constraint

solutions

Which of the following statements about linear programming models is true?

the algebraic and spreadsheet formulations of a linear programming model both have advantages

A resource-allocation problem requires information about

the amount of each resource used by each activity; the amount of each resource available

Construction of a benefit constraint requires data concerning

the contribution of each activity to each benefit

In a product mix problem, it is often difficult to estimate

the cost of new raw materials profitability of new products

In a resource allocation problem, the resource constraints are used to represent

the limited availability of some resource

which of the following is not an element of the product-mix problem?

the marketing budget for each product

if the total change (as a percentage of the allowable change) for two or more changes to objective function coefficients is more than 100 percent.

the optimal solution may or may not change

the feasible region constraints

the optimal solution; solutions that satisfy all constraint

In a transportation problem, the level of activities represents

the quantity shipped from each source to each destination

Managers can structure decisions as either a resource-allocation problem or as a cost-benefit-trade-off problem

true

Which of the following are benefits of what-if anaylysis?

understanding the impact of changes to managerial policies determining if a models solution is still valid after conditions change identifying sensitive parameters

Which of the following is a way to investigate the effect of simultaneous changes to objective function coefficients?

use a two-way parameter analysis report; try the changes directly on a spreadsheet model; apply the 100 percent rule

Resource constraints have the form "amount of resource _________ <= amount of resource _________

used; available

Model ______ involves testing early version of the model to identify errors and omissions

validation

if an analyst wants to know which model parameters are most sensitive to estimate errors, one approach is to use ___________- if analysis to evaluate parameter sensitivity

what

The process of using a model which has already identified an optimal solution to gain additional insight into the problem is known as

what-if analysis

the graphical method of solving a linear programming model can be used

when a problem involves only two decision variables