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
