564 Exam
A dummy origin in a transportation problem is used when supply exceeds demand. True False
False
The absolute value of the shadow price indicates the amount by which the objective function will be improved if the corresponding constraint is loosened. improved if the corresponding constraint is tightened. made worse if the corresponding constraint is loosened improved if the corresponding constraint is unchanged.
improved if the corresponding constraint is loosened. The absolute value of the shadow price indicates the amount by which the objective function will be improved if the corresponding constraint is loosened.
Assume an objective function has a value of 150 and the shadow price for resource 1 is 5 and the allowable increase for this resource is greater than 10. If 10 more units of resource 1 are added, what is the impact on the objective function value? increase of 50 increase of unknown amount decrease of 50 increase of 10
increase of 50 The shadow price for a constraint indicates the amount by which the objective function value changes given a unit increase in the RHS value of the constraint, assuming all other coefficients remain constant. Given an objective function value of 150 and a shadow price for resource 1 of 5, if 10 more units of resource 1 are added then the impact on the objective function value is an increase of 50 (shadow price for each unit of increase, or 5 X 10 = 50). This result is because the 10 unit increase is within the allowable range, since the allowable increase is greater than 10.
Which of the following is true regarding goal programming? The objective function is not useful when comparing goal programming solutions. We can place upper bounds on any of the deviation variables. A preemptive goal program involves deviations with arbitrarily large weights. All of these are true.
All of these are true.
Which of the following statements is NOT true? A feasible solution satisfies all constraints. An optimal solution satisfies all constraints. An infeasible solution violates all constraints. A feasible solution point does not have to lie on the boundary of the feasible region.
An infeasible solution violates all constraints. When there is not a solution that satisfies ALL constraints, the LP model is said to be infeasible.
Decision criteria __________ are the choices faced by the decision maker. are the problems faced by the decision maker. are the ways to evaluate the choices faced by the decision maker. must be unique for a problem.
Are the ways to evaluate the choices faced by the decision maker
The decision variables of a model are also known as the __________ uncontrollable output. controllable inputs. environmental factors. projected results.
Controllable Inputs
A transshipment problem will have nine decision variables when there are three sources, each connected to four destinations, through two transshipment nodes. True False
False
The constraint x1 − x2 = 0 implies that if project 1 is selected, project 2 cannot be. True False
False
An infeasible LP model can be fixed by changing the objective function. True False
False False. Infeasibility is independent of the objective function. Infeasibility arises when the constraints are too restrictive to allow for a feasible region—that is, some, or all, of the constraints cannot be satisfied. The only thing that can fix an infeasible LP is adjusting the constraints. The Feasibility Report will indicate which constraints were violated and need to be addressed.
Decision variables limit the degree to which the objective in a linear programming problem is satisfied. True False
False False. Only the constraints put any restrictions on the optimal solution.
__________ is the most critical step of the decision-making process.
Identifying and defining the problem
Which of the following are true regarding weights assigned to deviational variables? Larger weights are assigned to undesirable deviations from the respective goals. The weights assigned must sum to one. The weight assigned to the deviation under a particular goal must be the same as the weight assigned to the deviation above that particular goal. All weights must be nonzero.
Larger weights are assigned to undesirable deviations from the respective goals. A variable that represents a highly undesirable deviation from a particular goal is assigned a relatively large weight—making it highly undesirable for that variable to assume a value larger than 0. A variable that represents a neutral or desirable deviation from a particular goal is assigned a weight of 0 or some value lower than 0
In what part(s) of a linear programming formulation would the decision variables be stated? objective function and the left-hand side of each constraint objective function and the right-hand side of each constraint the left-hand side of each constraint only the objective function only
Objective function and the left-hand side of each constraint The decision variables must be included in the objective function and the LHS of each constraint. The RHS of the constraint will denote the limit on the specific resource in that constraint.
Which of the following analytical techniques helps us arrive at the best decision? Predictive analytics Data mining Prescriptive analytics Descriptive analytics
Prescriptive analytics
Data-driven decision making tends to decrease a firm's __________ market value. productivity. risk. profit.
Risk
Suppose that the first goal in a GP problem is to make 3 X 1 + 4 X 2 approximately equal to 36. Using the deviation variables d 1 − and d 1 +, what constraint can be used to express this goal?
This goal can be expressed by constraint:: 3 X 1 + 4 X 2 + d 1 − − d 1 + = 36
Which of the following states the objective of time series analysis? To predict the values of a time series based on one or more other variables To analyze the cause-and-effect relationship of a dependent variable with a time series and one or more other variables To use present variable values to study what should have been the ideal past values To uncover a pattern in a time series and then extrapolate the pattern into the future
To uncover a pattern in a time series and then extrapolate the pattern into the future
In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved. True False
True
In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables. True False
True A linear programming problem is defined by the linear relationship of the decision variables. If the relationship is not linear, we need to use a different type of mathematical programming technique in order to solve the problem.
When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is __________. positive zero negative infinite
Zero
The shadow price of a non-binding constraint is positive. zero. negative. indeterminate.
Zero The shadow price of a non-binding constraint is zero because the resource is abundant.
A normally distributed error term with a mean of zero would ___________. have values that are symmetric about the variance. allow more accurate modeling. yield biased regression estimates. be a hyperbolic curve.
allow more accurate modeling.
A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that an alternate optimal solution exists. an error in formulation has been made. the right hand sides should be increased. the objective function needs new coefficients.
an alternate optimal solution exists. If a variable has a final value equal to its simple lower or upper bound and a reduced cost of zero, an alternate optimal solution exists.
A causal model provides evidence of __________ between an independent variable and the variable to be forecast. a causal relationship an association no relationship a seasonal relationship
an association
The ___________ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation. residual coefficient of determination dummy variable interaction variable
coefficient of determination
Limited resources are modeled in optimization problems as ___________ an objective function. constraints. decision variables. alternatives.
constraints.
Suppose that X1 equals 4. What are the values for d 1 +and d 1 − in the following constraint? X 1 + d 1 − − d 1 + = 8 d 1 − = 4 a n d d 1 + = 0 d 1 − = 0 a n d d 1 + = 4 d 1 − = 4 a n d d 1 + = 4 d 1 − = 8 a n d d 1 + = 0
d 1 − = 4 a n d d 1 + = 0 If X1 equals 4, then L a T e X : d 1 − = 4 and L a T e X : d 1 + = 0 in order for the constraint L a T e X : X 1 + d 1 − − d 1 + = 8to be true.
A manager wants to ensure that he does not exceed his budget by more than $1,000 in a goal programming problem. If the budget constraint is the third constraint in the goal programming problem, which of the following formulas will best ensure that the manager's objective is met? M I N d3 + d 3 − ≥ 1 , 000 d 3 + = 1 , 000 d 3 + ≤ 1 , 000
d 3 + ≤ 1 , 000
In a linear regression model, the variable that is being predicted or explained is known as _____________. It is denoted by y and is often referred to as the response variable. dependent variable independent variable residual variable regression variable
dependent variable
A production optimization problem has 4 decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact? f (X1, X2, X3, X4) ≤ b1 f (X1, X2, X3, X4) ≥ b1 f (X1, X2, X3, X4) = b1 f (X1, X2, X3, X4) ≠ b1
f (X1, X2, X3, X4) ≥ b1 The right hand side value of the constraint, b1, imposes a lower limit on the value of the function f(.)
A constraint which cannot be violated is called a __________. binding constraint hard constraint definite constraint required constraint
hard constraint
Slack __________. is the difference between the left and right sides of a constraint is the amount by which the left side of a ≤ constraint is smaller than the right side is the amount by which the left side of a ≥ constraint is larger than the right side exists for each variable in a linear programming problem
is the amount by which the left side of a ≤ constraint is smaller than the right side
In a business, the values indicating the current operating characteristics, such as financial position, inventory on hand, and customer service metrics, are typically known as __________. company performance indicators performance indicators key performance indicators business performance indicators
key performance indicators
DJ needs to display data over time. Which of the following charts should he use? scatter chart pie chart bar chart line chart
line chart
The objective of the transportation problem is to __________. identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. minimize the number of origins used to satisfy total demand at the destinations. minimize the number of shipments necessary to satisfy total demand at the destinations. minimize the cost of shipping products from several origins to several destinations.
minimize the cost of shipping products from several origins to several destinations.
If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the optimal solution? increases by an unknown amount increases more than 0 but less than 150 no change decreases by an unknown amount
no change If the shadow price for a resource is 0 and 150 units of the resource are added, the optimal solution no change because the resource is abundant.
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the __________. optimal solution alternative solution range of optimality range of feasibility
range of optimality An alternative solution occurs in some instances for the same model parameters. The range of feasibility is the range of the RHS of each constraint for which the shadow price is valid.
With reference to time series data patterns, a cyclical pattern is the component of the time series that __________. shows a periodic pattern lasting one year or less. does not vary with respect to time. shows a periodic pattern lasting more than one year. is characterized by a linear variation of the dependent variable with respect to time.
shows a periodic pattern lasting more than one year.
The allowable increase for a constraint is how many more units of a resource to purchase to maximize profits. the amount by which the resource can increase given shadow price. how much resource to use to get the optimal solution. the amount by which the constraint coefficient can increase without changing the final optimal value.
the amount by which the resource can increase given shadow price.
A binding greater than or equal to (≥) constraint in a minimization problem means that the variable is up against an upper limit. the minimum requirement for the constraint has just been met. another constraint is limiting the solution. the shadow price for the constraint will be positive.
the minimum requirement for the constraint has just been met.
Tables should be used instead of charts when __________ the reader needs relative comparisons of data. there are more than two columns of data. the values being displayed have different units or very different magnitudes. the reader need not differentiate the columns and rows.
the values being displayed have different units or very different magnitudes.
If a time series plot exhibits a horizontal pattern, then ___________. it is evident that the time series is stationary. the data fluctuates around the variable mean. there is no relationship between time and the time series variable. there is still not enough evidence to conclude that the time series is stationary.
there is still not enough evidence to conclude that the time series is stationary.
Goal programming differs from linear programming or integer linear programming in that __________. goal programming provides for multiple objectives goal programming excludes hard constraints with goal programming we iterate until an acceptable solution is obtained goal programming requires fewer variables
with goal programming we iterate until an acceptable solution is obtained
Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done? x1 + x2 = 1 x1 + x2 = 2 x1 − x2 ≤ 0 x1 − x2 ≥ 0
x1 − x2 ≥ 0 Correct. The conditions that satisfy this constraint: 1) Both projects are build, x1 = 1 and x2 = 1 and x1−x2 ≥ 0 or 2) Only project 1 is built, x1 = 1 and x2 = 0 and x1−x2 ≥ 0. Project 2 cannot alone and still satisfy this constraint.
