Manual simulation is limited because of the amount of real time required to simulate
even one trial.
Shorter-period moving averages react more slowly to recent demand changes than do
longer-period moving averages.
An opportunity cost table is developed by first subtracting the minimum value in each
row from all other row values and then repeating this process for each column.
If a nonlinear program has been correctly formulated, procedures guarantee a solution.
The service level is the probability that the inventory available during lead time will
meet demand.
The source node is the input node in a maximal flow problem.
In solving a linear programming problem with simplex method, the number of basic
variables is the same as the number of constraints in the original problem.
When earliest finish is subtracted from latest finish, we obtain the slack value for the
activity.
It is not possible to solve a transportation problem that has ≤ instead of = signs for the
supply constraints.
Project crashing is a method for shortening the project completion time by reducing the
completion time of one or more critical activities at a cost.
Simulations should always be started with an empty system.
In a balanced transportation model where supply equals demand, all constraints are
inequalities.
Probability trees are used only to compute conditional probabilities.
When using a linear programming model to solve the diet problem, the objective is
generally to maximize nutritional content.
The arrival rate is most frequently described by a negative exponential distribution.
The critical path activities have no slack.
Sensitivity analysis determines how a change in a parameter affects the optimal
solution.
In solving a maximization problem, the optimal profit associated with the relaxed
solution (LP-relaxation) is always less than or equal to the value of the optimal profit
associated with the integer solution.
In an unbalanced transportation model, supply does not equal demand, and supply
constraints have ≤ signs.
The maximin approach involves choosing the alternative with the highest payoff.
A trend is a gradual, long-term, up-or-down movement of demand.
A linear programming model solution with no integer restrictions is called a relaxed
solution.
A feasible solution is ensured by rounding down integer solution values.
Fixed cost is the difference between total cost and total variable cost.
Regardless of the number of nodes in a network, the minimal spanning tree always
contains the two nodes with the shortest distance between them.
Determining project completion time is an element of project planning.
Assignments are made to locations with 1 in the opportunity cost table.
A table of random numbers must be normally distributed and efficiently generated.
Management science techniques focus primarily on observation, model construction,
and implementation to find an appropriate solution to a problem.
A typical objective function might be written as 3S + 2R + 5Z ≤20
When using decision trees, branches with the greatest expected value are selected.
A normally distributed random variable has a mean of zero and a standard deviation of
one.
Let xij= gallons of component i used in gasoline j. Assume that we have two
components and two types of gasoline. There are 8000 gallons of component 1
available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons,
respectively. Write the supply constraint for component 1.
A) x21 + x22 ≤ 8000
B) x12 + x22 ≥ 8000
C) x11 + x12 ≤ 8000
D) x21 + x22 ≥ 8000
Consider the following project.
Determine the slack for activity D.
A) 2 days
B) 4 days
C) 6 days
D) 5 days
A professor would like to assign grades such that 7% of students receive Fs. If the exam
average is 62 with a standard deviation of 13, what grade should be the cutoff for an F?
(Round your answer.)
A) 43
B) 49
C) 50
D) 55
Consider the following project.
A dummy activity in a PERT network allows us to:
A) specify the positive time and resources required to complete the activity.
B) maintain the precedence relationships.
C) add more starting nodes.
D) add more ending nodes.
Suppose the landlord really wants the back door to be installed. For too long he has had
to cut through the garage and he figures when he retires, this house will be a perfect
downsize home for him to move into. How should the constraint for the back door be
written if he uses the following scheme for decision variables?
A) x5 + x6 ≤ 1
B) x5 + x6 = 1
C) x5 – x6 ≤ 1
D) x5 – x6 = 1
Zevon Enterprises
Zevon Enterprises provides services for clients worldwide and to protect all parties to
this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of
these services has its own special mix of needs for the resources the company has at its
disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2
product requires two lawyers, five guns, and $4,000; and the X3 product requires four
lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and
$15,000,000. For ease of conversation, Zevon employees usually speak about dollars as
“per thousand” so one of them asking for $7 means that they really need $7,000.
Zevon’s demand is variable depending on what they charge for it. For example, the X1
product’s demand is 200 – 2.25p1. The demand for X2 is 300 – 3p2, and the demand for
X3 is 400 – 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting
the per unit cost from the sales price, so for X1, the profit is p1 – 25, for X2 the profit is
p2– 3, and for X3 the profit is p3– 3.5.
The model is entered in Excel and the sensitivity report reveals that all of the
constraints’ Lagrange multipliers are zero. The impact for Zevon is:
A) The profit for this scenario cannot be maximized.
B) Not all of the lawyers they have available will be used.
C) The demand for service X1 exceeds Zevon’s ability to supply it.
D) The profit generated by service X1 is not a function of demand for X1.
In an assignment problem:
A) one agent can do parts of several tasks.
B) one task can be done by only one agent.
C) each agent is assigned to its own best task.
D) all of the above
A company has a goal to maintain the current employment level, but places more
importance on laying employees off than on hiring new employees. In other words, the
company would rather hire than lay off employees. If the company assigns a “penalty
weight” of 4 for the amount under the employment goal (goal 2) and a weight of 2 for
the amount over the employment goal, how would this be expressed in the objective
function?
A) Min 4P2d2
– + 2P2d2
+
B) Min 2P2d2
– + 4P2d2
+
C) Max 4P2d2
– + 2P2d2
+
D) Min 4P2d2
+ + 2P2d2
–
Jolt – K
The soda machine outside the lecture hall sees a steady stream of customers throughout
the day. The machine takes 4 seconds to deliver a can of carbonated sugar water once
the button is pressed and students generally know what they want from the machine –
the average feeding of the machine takes two seconds. Over the course of a twelve hour
lecture day, students arrive at the rate of 500 per hour.
Josie likes to tweet almost as much as she enjoys an ice cold soda. If she can type at the
rate of two characters per second, how many full tweets can she send out while waiting
in line for a soda? Assume that Josie’s tweets always completely fill the maximum
number of twitter characters.
A) Josie can send about a third of a tweet.
B) Josie can send about a half a tweet.
C) Josie can send about three-fourths of a tweet.
D)Josie can send one tweet.
Random numbers generated by a ________ process instead of a ________ process are
pseudorandom numbers.
A) physical, physical
B) physical, mathematical
C) mathematical, physical
D) mathematical, mathematical
Deviational variables in a goal programming model constraint represent the:
A) underachievement or overachievement of a goal level.
B) resource constraint as defined by the linear model.
C) probability of an optimal solution.
D) probabilistic variables in the objective constraints.
The poultry farmer has in mind the following levels for each of his metrics of interest: a
plumage score greater than 75, fertilizer production greater than 80 ounces per week,
temperament less than 100 decibels, and an appetite less than 160 ounces of layer
pellets per week. When he runs his linear programming model, he discovers that his
flock will consist entirely of Leghorn birds. He can picture the sad little faces of his
children when he tells them that there will be no variety of birds gracing their front
lawn this summer. Help him avoid the embarrassment by selecting a constraint that will
ensure that there is some variety in his flock.
A) 5L + 4C + 8B ≤ 160
B) 5L + 4C + 8B ≥ 160
C) C + B ≥ 5
D) L + C + B ≥ 5
Jolt – K
The soda machine outside the lecture hall sees a steady stream of customers throughout
the day. The machine takes 4 seconds to deliver a can of carbonated sugar water once
the button is pressed and students generally know what they want from the machine –
the average feeding of the machine takes two seconds. Over the course of a twelve hour
lecture day, students arrive at the rate of 500 per hour.
How long is the average wait at the soda machine?
A) 15 seconds
B) 20 seconds
C) 25 seconds
D) 30 seconds
The simplex method ________ guarantee integer solutions.
A) sometimes does
B) does
C) does not
D) may
Multiple optimal solutions provide ________ flexibility to the decision maker.
A) greater
B) less
C) greater or equal
D) less or equal
A technique that assumes certainty in its solution is referred to as:
A) stochastic.
B) probabilistic.
C) deterministic.
D) parametric.
It was a house with seven cats, four female and three male, and the litterbox was busier
than O’Hare Airport during the week of Thanksgiving. The beleaguered husband’s home
office was right around the corner from the laundry room, where the litterbox was kept,
and heard three separate instances of use. What is the likelihood that all of the instances
were the work of the male cats?
A) .079
B) .187
C) .429
D) .314
The type of linear program that compares services to indicate which one is less
productive or inefficient is called:
A) product mix.
B) data envelopment analysis.
C) marketing.
D) blending.
Queuing system operating statistics:
A) change from start to finish during the day.
B) are constant over time.
C) include queue discipline, arrival rate, and service rate.
D) all of the above
Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a
period of one month and assigned them to five different categories as shown in the
table.
What is the duration of Mr. Lane’s expected commute?
A) 5 minutes
B) 25 minutes
C) 5 minutes
D) 75 minutes
________ moving averages react more slowly to recent demand changes than do
________ moving averages.
A) Longer-period, shorter-period
B) Shorter-period, longer-period
C) Longer-period, longer-period
D) Shorter-period, shorter-period
A baker uses organic flour from a local farmer in all of his baked goods. For each batch
of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds,
and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with
no more than 24 pounds per week. The constraint that represents this condition is:
A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8
B) x1 + x2 + x3 ≥24
C) x1 + x2 + x3 ≤24
D) 4x1 + 3x2 + 2x3 ≤ 24.
In assigning random numbers to probabilistic events in a simulation:
A) several events are associated with the same random number.
B) every random number is associated with a particular event.
C) every event is associated with the same random number.
D) the events dictate the seed number of the random number stream.
Riverside Industries makes two products and each product is processed in three
departments. The time requirements for each product in each department are given
below. The profit for each product is also provided as well as the available hours in
each department.
Product Department A Department B Department C Profit
1 3 4 2 1
2 2 1 2 2
Available Hours 600 400 400
Management wants to achieve three goals. The first two goals are equal in priority.
Priority 1: Produce at least 125 units of product 1.
Priority 1: Produce at least 80 units of product 2.
Priority 2: Achieve a profit of at least 300.
The objective function for this goal program is:
A) Min P1d1
– + P1d2
–, P2d3
–.
B) Min P1d1
+ + P1d2
–,P2d3
–.
C) Min P1d1
– + P1d2
+, P2d33
–.
D) Min P1d1
– + P1d2
–, P2d3
+.
In a(n) ________ inventory system, an order is placed for a variable amount after a
fixed passage of time.
A) periodic
B) continuous
C) optimal
D) economic
Regret is the difference between the payoff from the:
A) best decision and all other decision payoffs.
B) worst decision and all other decision payoffs.
C) best decision and the worst decision payoffs.
D) none of the above
Consider the following integer LP.
MAX + 5
subject to: + 10 ≤ 20
≤ 2
, ≥ 0 and integer
Solve for the value of x2 at the first node and identify the constraint below that correctly
represents one of the descendant branches.
A) x2 ≥ 1
B) x2 ≤ 1
C) x2 ≤ 2
D) x2 ≥ 0
A large book publisher has five manuscripts that must be edited as soon as possible.
Five editors are available for doing the work, however their working times on the
various manuscripts will differ based on their backgrounds and interests. The publisher
wants to use an assignment method to determine who does what manuscript. Estimates
of editing times (in hours) for each manuscript by each editor is:
a) How many supply-side constraints are needed?
b) How many demand-side constraints are needed?
c) How many variables are involved in this assignment method?
The optimal integer solution will always be between the upper bound of the ________
solution and a lower bound of the rounded-down ________ solution.
A) relaxed, non-integer
B) integer, relaxed
C) relaxed, integer
D) none of the above
A ________ is a plan of action followed by a player.
A) game situation
B) strategy
C) value of the game
D) best strategy
E) pure strategy
Consider the following demand and forecast.
If MAD = 2 for the four periods under consideration, what is the forecast for period 4?
A) 19
B) 20
C) 21
D) 22
The events in an experiment are ________ if only one can occur at a time.
A) mutually exclusive
B) non-mutually exclusive
C) mutually inclusive
D) independent
The only car dealership in a community stocks cars from two manufacturers, Fret and
Cessy. The following transition matrix shows the probabilities of a customer purchasing
each brand of car in the next year given that he or she purchased that car in the current
year.
Determine the steady state probabilities for Fret and Cessy.
A) .875, .125
B) .645, .355
C) .621, .379
D) .571, .429
E) .55, .45
The department chair looks at past course evaluations and realizes that if she wants to
attract students to the Operations and Supply Chain major, it would be best if Geoff
were never assigned to teach that class. How can her standard model be modified to
ensure that Geoff cannot scare away students from the major?
When applying linear programming models to project planning, the objective is to
minimize ________.
Write the assignment problem matrix below as a network flow problem. Assume that
the numbers in each cell represent the travel distance required between nodes. The dash
indicates that there is not a route between nodes.
If events A and B are independent, then P(AB) = ________.
Two psychology majors, in two different sections of Clinical Psychology, were
comparing test scores. The following gives the students’ scores, class mean, and
standard deviation for each section:
Section 1 Section 2
Student score 84 75
Mean 75 60
Standard deviation 7 8
The weight of a loaf of bread is normally distributed with a mean of 22 oz and a
standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz?
Project ________ is a method for shortening the project completion time by reducing
the completion time of one or more critical activities at a cost.
The only car dealership in a community stocks cars from two manufacturers, Fret and
Cessy. The following transition matrix shows the probabilities of a customer purchasing
each brand of car in the next year given that he or she purchased that car in the current
year.
Given that a customer purchased the brand Cessy in the present year (year 1), determine
the probability that a customer will purchase Fret in year 3.
As customers move through a processing center line they first wait in the reception
room, then they fill in some personal information on a tablet PC once one becomes
available. Finally, they head to another waiting area before submitting a sample. This
queuing system is ________.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer.
Wiethoff has four Different machines that can produce this kind of hose. Because these
machines are from Different manufacturers and use Differing technologies, their
specifications are not the same.
Write a constraint that will ensure that Weithoff purchases exactly two machines.
The Monte Carlo process is analogous to and derives its name from ________.
A ________ occurs when an item is out of stock and is sold to the customer when a
shipment arrives.
Two companies are about to make a decision regarding an investment in a new
promotional campaign. Company A will either advertise in all media or advertise in
newspapers only. Company B will either run a sweepstake or run a big sale. The payoff
matrix is shown below.
Using the information above, determine the value of the game.
The ________ is the sum of the absolute value of forecasting errors divided by the
number of periods in which a forecast was made.
The production manager for the Rusty soft drink company is considering the production
of two kinds of soft drinks: regular and diet. Two of her resources are constraint
production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients),
limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5
gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for
regular soft drink are $3 per case and profits for diet soft drink are $2 per case. What
are optimal daily profits?
Almost all of the data from a normal distribution fall within ________ standard
deviations of the mean.
In order to prevent the accumulation of inventory at transshipment points, they should
be modeled as being ________ nodes.
Napoleon is contemplating four institutions of higher learning as options for a Masters
in Business Administration. Each university has strong and weak points and the demand
for MBA graduates is uncertain. The availability of jobs, student loans, and financial
support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and
Seattle University have comparatively high tuition, which would necessitate Napoleon
take out student loans resulting in possibly substantial student loan debt. In a tight
market, degrees with that cachet might spell the difference between a hefty paycheck
and a piddling unemployment check. Northeastern State University and Texas Tech
University hold the advantage of comparatively low tuition but a more regional appeal
in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist
with the decision. Together they forecast three possible scenarios for the job market and
institutional success and predict annual cash flows associated with an MBA from each
institution. All cash flows in the table are in thousands of dollars.
Summer bursts into the meeting and announces that there’s another way to consider the
issue. Since Napoleon will have to live with his choice for the rest of his life, he might
consider selecting the alternative that will cause him the least pain in hindsight when he
compares his outcome with what he might have gained. Which criterion is she talking
about, what is the best school for this criterion, and why?
In a linear programming formulation of a transportation model, each of the possible
combinations of supply and demand locations is a(n) ________.
The ________ property of linear programming models indicates that the rate of change,
or slope, of the objective function or a constraint is constant.