BMDS 3371 Week 5 Midterm Exam Answers
BMDS 3371 Week 5 Midterm Exam
Answers
UIW Online Spring II 2015 BMDS
3371 Midterm
Name:
04/03/15
Each question is worth
2.5 points. The midterm covers chapters 2, 3, 4 and 6.
The midterm is due
by Wednesday, April 8, 2015, 11:59pm CST. No exceptions!
You may print the
midterm, highlight the answers, scan and upload it, or,
you may highlight the
answers using the Word feature and then submit it.
Make sure to include
your last name when saving the file. E.g. Fiala_Midterm
1. The maximization or minimization of a quantity
is the
|
a.
|
goal of management
science.
|
|
b.
|
decision for
decision analysis.
|
|
c.
|
constraint of
operations research.
|
|
d.
|
objective of linear
programming.
|
2. Decision variables
|
a.
|
tell how much or how
many of something to produce, invest, purchase, hire, etc.
|
|
b.
|
represent the values
of the constraints.
|
|
c.
|
measure the
objective function.
|
|
d.
|
must exist for each
constraint.
|
3. Which of the following is a valid objective
function for a linear programming problem?
|
a.
|
Max 5xy
|
|
b.
|
Min 4x + 3y + (2/3)z
|
|
c.
|
Max 5x2 + 6y2
|
|
d.
|
Min (x1 + x2)/x3
|
4. Which of the following statements is NOT true?
|
a.
|
A feasible solution
satisfies all constraints.
|
|
b.
|
An optimal solution
satisfies all constraints.
|
|
c.
|
An infeasible
solution violates all constraints.
|
|
d.
|
A feasible solution
point does not have to lie on the boundary of the feasible region.
|
5. A solution that satisfies all the constraints
of a linear programming problem except the nonnegativity constraints is called
|
a.
|
optimal.
|
|
b.
|
feasible.
|
|
c.
|
infeasible.
|
|
d.
|
semi-feasible.
|
6.
Slack
|
a.
|
is the difference between
the left and right sides of a constraint.
|
|
b.
|
is the amount by
which the left side of a £ constraint is smaller than the right side.
|
|
c.
|
is the amount by
which the left side of a ³ constraint is larger than the right side.
|
|
d.
|
exists for each variable
in a linear programming problem.
|
7. To find the optimal solution to a linear
programming problem using the graphical method
|
a.
|
find the feasible
point that is the farthest away from the origin.
|
|
b.
|
find the feasible
point that is at the highest location.
|
|
c.
|
find the feasible
point that is closest to the origin.
|
|
d.
|
None of the
alternatives is correct.
|
8. Which of the following special cases does not
require reformulation of the problem in order to obtain a solution?
|
a.
|
alternate optimality
|
|
b.
|
Infeasibility
|
|
c.
|
Unboundedness
|
|
d.
|
each case requires a
reformulation.
|
9. The improvement in the value of the objective
function per unit increase in a right-hand side is the
|
a.
|
sensitivity value.
|
|
b.
|
dual price.
|
|
c.
|
constraint
coefficient.
|
|
d.
|
slack value.
|
10. As long as the slope of the objective function
stays between the slopes of the binding constraints
|
a.
|
the value of the
objective function won’t change.
|
|
b.
|
there will be
alternative optimal solutions.
|
|
c.
|
the values of the
dual variables won’t change.
|
|
d.
|
there will be no
slack in the solution.
|
11. Infeasibility means that the number of
solutions to the linear programming models that satisfies all constraints is
|
a.
|
at least 1.
|
|
b.
|
0.
|
|
c.
|
an infinite number.
|
|
d.
|
at least 2.
|
12. A constraint that does not affect the feasible
region is a
|
a.
|
non-negativity
constraint.
|
|
b.
|
redundant
constraint.
|
|
c.
|
standard constraint.
|
|
d.
|
slack constraint.
|
13. Whenever all the constraints in a linear
program are expressed as equalities, the linear program is said to be written
in
|
a.
|
standard form.
|
|
b.
|
bounded form.
|
|
c.
|
feasible form.
|
|
d.
|
alternative form.
|
14. All of the following statements about a
redundant constraint are correct EXCEPT
|
a.
|
A redundant
constraint does not affect the optimal solution.
|
|
b.
|
A redundant constraint
does not affect the feasible region.
|
|
c.
|
Recognizing a
redundant constraint is easy with the graphical solution method.
|
|
d.
|
At the optimal
solution, a redundant constraint will have zero slack.
|
15. All linear programming problems have all of
the following properties EXCEPT
|
a.
|
a linear objective
function that is to be maximized or minimized.
|
|
b.
|
a set of linear
constraints.
|
|
c.
|
alternative optimal
solutions.
|
|
d.
|
variables that are
all restricted to nonnegative values.
|
16. To solve a linear programming problem with
thousands of variables and constraints
|
a.
|
a personal computer
can be used.
|
|
b.
|
a mainframe computer
is required.
|
|
c.
|
the problem must be
partitioned into subparts.
|
|
d.
|
unique software
would need to be developed.
|
17. A negative dual price for a constraint in a
minimization problem means
|
a.
|
as the right-hand
side increases, the objective function value will increase.
|
|
b.
|
as the right-hand
side decreases, the objective function value will increase.
|
|
c.
|
as the right-hand
side increases, the objective function value will decrease.
|
|
d.
|
as the right-hand
side decreases, the objective function value will decrease.
|
18. If a decision variable is not positive in the
optimal solution, its reduced cost is
|
a.
|
what its objective
function value would need to be before it could become positive.
|
|
b.
|
the amount its
objective function value would need to improve before it could become
positive.
|
|
c.
|
zero.
|
|
d.
|
its dual price.
|
19. A constraint with a positive slack value
|
a.
|
will have a positive
dual price.
|
|
b.
|
will have a negative
dual price.
|
|
c.
|
will have a dual
price of zero.
|
|
d.
|
has no restrictions
for its dual price.
|
20. The amount by which an objective function
coefficient can change before a different set of values for the decision
variables becomes optimal is the
|
a.
|
optimal solution.
|
|
b.
|
dual solution.
|
|
c.
|
range of optimality.
|
|
d.
|
range of
feasibility.
|
21. The range of feasibility measures
|
a.
|
the right-hand-side
values for which the objective function value will not change.
|
|
b.
|
the right-hand-side values
for which the values of the decision variables will not change.
|
|
c.
|
the right-hand-side
values for which the dual prices will not change.
|
|
d.
|
each of these
choices are true.
|
22. The 100% Rule compares
|
a.
|
proposed changes to
allowed changes.
|
|
b.
|
new values to
original values.
|
|
c.
|
objective function
changes to right-hand side changes.
|
|
d.
|
dual prices to
reduced costs.
|
23. An objective function reflects the relevant
cost of labor hours used in production rather than treating them as a sunk
cost. The correct interpretation of the dual price associated with the labor
hours constraint is
|
a.
|
the maximum premium
(say for overtime) over the normal price that the company would be willing to
pay.
|
|
b.
|
the upper limit on
the total hourly wage the company would pay.
|
|
c.
|
the reduction in
hours that could be sustained before the solution would change.
|
|
d.
|
the number of hours
by which the right-hand side can change before there is a change in the
solution point.
|
24. A section of output from The Management
Scientist is shown here.
|
Variable
|
Lower Limit
|
Current Value
|
Upper Limit
|
|
1
|
60
|
100
|
120
|
What will happen to
the solution if the objective function coefficient for variable 1 decreases by
20?
|
a.
|
Nothing. The values
of the decision variables, the dual prices, and the objective function will
all remain the same.
|
|
b.
|
The value of the
objective function will change, but the values of the decision variables and
the dual prices will remain the same.
|
|
c.
|
The same decision
variables will be positive, but their values, the objective function value,
and the dual prices will change.
|
|
d.
|
The problem will
need to be resolved to find the new optimal solution and dual price.
|
25. A section of output from The Management
Scientist is shown here.
|
Constraint
|
Lower Limit
|
Current Value
|
Upper Limit
|
|
2
|
240
|
300
|
420
|
What will happen if
the right-hand-side for constraint 2 increases by 200?
|
a.
|
Nothing. The values
of the decision variables, the dual prices, and the objective function will
all remain the same.
|
|
b.
|
The value of the
objective function will change, but the values of the decision variables and
the dual prices will remain the same.
|
|
c.
|
The same decision
variables will be positive, but their values, the objective function value,
and the dual prices will change.
|
|
d.
|
The problem will
need to be resolved to find the new optimal solution and dual price.
|
26. The dual value on the nonnegativitiy
constraint for a variable is that variable’s
|
a.
|
sunk cost.
|
|
b.
|
surplus value.
|
|
c.
|
reduced cost.
|
|
d.
|
relevant cost.
|
27. The dual price measures, per unit increase in
the right hand side of the constraint,
|
a.
|
the increase in the
value of the optimal solution.
|
|
b.
|
the decrease in the
value of the optimal solution.
|
|
c.
|
the improvement in
the value of the optimal solution.
|
|
d.
|
the change in the
value of the optimal solution.
|
28. Sensitivity analysis information in computer
output is based on the assumption of
|
a.
|
no coefficient
changes.
|
|
b.
|
one coefficient
changes.
|
|
c.
|
two coefficients
change.
|
|
d.
|
all coefficients
change.
|
29. When the cost of a resource is sunk, then the
dual price can be interpreted as the
|
a.
|
minimum amount the
firm should be willing to pay for one additional unit of the resource.
|
|
b.
|
maximum amount the
firm should be willing to pay for one additional unit of the resource.
|
|
c.
|
minimum amount the
firm should be willing to pay for multiple additional units of the resource.
|
|
d.
|
maximum amount the
firm should be willing to pay for multiple additional units of the resource.
|
30. Which of the following is not a question
answered by sensitivity analysis?
|
a.
|
If the right-hand
side value of a constraint changes, will the objective function value change?
|
|
b.
|
Over what range can
a constraint’s right-hand side value without the constraint’s dual price
possibly changing?
|
|
c.
|
By how much will the
objective function value change if the right-hand side value of a constraint
changes beyond the range of feasibility?
|
|
d.
|
By how much will the
objective function value change if a decision variable’s coefficient in the
objective function changes within the range of optimality?
|
31. Media selection problems usually determine
|
a.
|
how many times to
use each media source.
|
|
b.
|
the coverage
provided by each media source.
|
|
c.
|
the cost of each
advertising exposure.
|
|
d.
|
the relative value
of each medium.
|
32. To study consumer characteristics, attitudes,
and preferences, a company would engage in
|
a.
|
client satisfaction
processing.
|
|
b.
|
marketing research.
|
|
c.
|
capital budgeting.
|
|
d.
|
production planning.
|
33. The dual price for a constraint that compares
funds used with funds available is .058. This means that
|
a.
|
the cost of
additional funds is 5.8%.
|
|
b.
|
if more funds can be
obtained at a rate of 5.5%, some should be.
|
|
c.
|
no more funds are
needed.
|
|
d.
|
the objective was to
minimize.
|
34. Let M be the number of units to make and B be
the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit
and 4000 units are needed, the objective function is
|
a.
|
Max 2M + 3B
|
|
b.
|
Min 4000 (M + B)
|
|
c.
|
Max 8000M + 12000B
|
|
d.
|
Min 2M + 3B
|
35. Modern revenue management systems maximize
revenue potential for an organization by helping to manage
|
a.
|
pricing strategies.
|
|
b.
|
reservation
policies.
|
|
c.
|
short-term supply
decisions.
|
|
d.
|
All of the
alternatives are correct.
|
36. The problem which deals with the distribution
of goods from several sources to several destinations is the
|
a.
|
maximal flow problem
|
|
b.
|
transportation
problem
|
|
c.
|
assignment problem
|
|
d.
|
shortest-route
problem
|
37. The parts of a network that represent the
origins are
|
a.
|
the capacities
|
|
b.
|
the flows
|
|
c.
|
the nodes
|
|
d.
|
the arcs
|
38. The objective of the transportation problem is
to
|
a.
|
identify one origin
that can satisfy total demand at the destinations and at the same time
minimize total shipping cost.
|
|
b.
|
minimize the number
of origins used to satisfy total demand at the destinations.
|
|
c.
|
minimize the number
of shipments necessary to satisfy total demand at the destinations.
|
|
d.
|
minimize the cost of
shipping products from several origins to several destinations.
|
39. The number of units shipped from origin i to
destination j is represented by
|
a.
|
xij.
|
|
b.
|
xji.
|
|
c.
|
cij.
|
|
d.
|
cji.
|
40. Which of the following is not true regarding
the linear programming formulation of a transportation problem?
|
a.
|
Costs appear only in
the objective function.
|
|
b.
|
The number of
variables is (number of origins) x (number of destinations).
|
|
c.
|
The number of
constraints is (number of origins) x (number of destinations).
|
|
d.
|
The constraints’
left-hand side coefficients are either 0 or 1.
|
No comments:
Post a Comment