Nodes represent junction points connecting branches.
Events are mutually exclusive if one, and only one, can occur at a time.
If the number of unique assignments is less than the number of rows or columns, a line
test must be used.
A payoff table is a means of organizing a decision situation, including the payoffs from
different decisions given the various states of nature.
In a zero-sum game, one player’s gains represent another’s exact losses.
When the number of people and the number of tasks are not equal in an assignment
problem then the problem cannot be solved.
In a media selection problem, instead of having an objective of maximizing profit or
minimizing cost, generally the objective is to maximize the audience exposure.
A conditional constraint specifies the conditions under which variables are integers or
real variables.
Assignments are made to locations with 0 in the opportunity cost table.
If a business frequently runs out of inventory, their service levels are negative.
The equal likelihood criterion assigns a probability of 0.5 to each state of nature.
The Hurwicz criterion multiplies the best payoff by the coefficient of optimism.
Decision Support Systems (DSS) use computers to help decision makers address
complex problems.
Goal programming violates the divisibility property of linear programming.
In PERT, three time estimates (optimistic, most likely, and pessimistic) provide an
estimate of the mean and variance for each activity, based on the normal distribution.
Objective probabilities that can be stated prior to the occurrence of an event are
classical or a priori.
Final tableaus cannot be used to conduct sensitivity analysis.
When using branch and bound for a maximization integer programming problem, the
lower bound at the initial node can always be determined by rounding down the LP
relaxation solution values regardless of the types of constraints in the problem.
The Lagrangian function is the original objective function plus the Lagrange multiplier
times the difference of the left and right sides of the constraint.
A conservative approach to a balanced transportation model would be to make all
constraints less-than-or-equal-to constraints.
In a transportation problem, items are allocated from sources to destinations at a
maximum value.
The critical path is the shortest path through the project network.
The payoffs for a mixed strategy game assumes that the game is played exactly one
time.
In a transshipment problem, items may be transported directly from sources to
destinations.
Relative frequency is the more widely used definition of objective probability.
Slack variables are only associated with maximization problems.
If service level is 50%, then safety stock is equal to 50% of lead time demand.
In a pure strategy game, each player adopts a single strategy as an optimal strategy.
When the branch and bound approach is applied to an integer programming problem, it
is used in conjunction with the normal non-integer solution approach.
The theoretical limit on the number of decision variables that can be handled by the
simplex method is 50.
One goal is never achieved at the expense of another higher-priority goal.
Simulation applies mathematical models to determine optimal solutions to business
problems.
When using the graphical method, only one of the four quadrants of an xy-axis needs to
be drawn.
Maximum profit is achieved everywhere the first derivative of the profit function equals
zero.
Calling populations are always finite.
One type of constraint in an integer program is a multiple-choice constraint.
The transportation model is a special type of linear regression model.
Armed only with his fingers, the owner decides that the safest forecasting approach is a
weighted moving average using 0.6, 0.3, and 1 for the most recent three. Generate a
forecast for the year using this technique and then calculate forecast errors using
MAPD. What is the mean absolute deviation for this forecasting approach?
A) 5.33%
B) 8.94%
C) 6.36%
D) 7.73%
________ is absolute error as a percentage of demand.
A) Cumulative error
B) MAD
C) MAPD
D) Average error
Use the following information to answer the question(s) below.
Participants eligible for a retraining program can be in one of four states:
A – not in the training program
B – discharged
C – in training
D – employed
You are given the following transition matrix and the fundamental matrix.
Assume that there were initially 10 people not in the training program (State A) and 60
people who were in the training program (State C). Approximately how many people
will end up being discharged?
A) 10
B) 15
C) 40
D) 55
E) 60
The problem that deals with the distribution of goods from several sources to several
destinations is the:
A) network problem.
B) assignment problem.
C) transportation problem .
D) transshipment problem.
Jim is considering pursuing an MS in Information Systems degree. He has applied to
two different universities. The acceptance rate for applicants with similar qualifications
is 20% for University X and 45% for University Y. What is the probability that Jim will
be accepted at both universities?
A) .65
B) .25
C) .20
D) .09
Without satisfying the non-negativity constraint, a solution that satisfies all the other
constraints of a linear programming problem is called:
A) feasible.
B) infeasible.
C) semi-feasible.
D) optimal.
The metropolitan airport commission is considering the establishment of limitations on
noise pollution around a local airport. At the present time, the noise level per jet takeoff
in one neighborhood near the airport is approximately normally distributed with a mean
of 100 decibels and a standard deviation of 3 decibels. What is the probability that a
randomly selected jet will generate a noise level of more than 105 decibels?
A) 0.0228
B) 0.0475
C) 0.0485
D) 0.0500
A model is a functional relationship that includes:
A) variables.
B) parameters.
C) equations.
D) all of the above
The Krewe of Orpheus
The Krewe of Orpheus maintains a supply of swizzle sticks for events throughout the
year. Demand for swizzle sticks is shockingly low, a quick check of krewe records from
last year reveals that they used only 585,000, but the krewe president believes that they
should be good stewards of what they have, so they seek to manage this inventory using
the EOQ policy, although they prefer to refer to it as an EOKrewe policy for obvious
reasons. Swizzle sticks are not expensive items, they cost a nickel apiece largely due to
the club logo printed on each one. This also serves to increase the lead time as they
can’t be obtained from a standard restaurant supply house. Instead, they must be ordered
with an eye towards the six day lead time. It costs $15 to place an order, most of this
cost is a result of explaining the meaning of “Laissez les bons temps rouler” and why it
should be printed on the edge of each swizzle stick. Holding cost is 20% of purchase
price.
What is the average inventory if they order at their EOKrewe quantity?
A) 41892
B) 20946
C) 18374
D) 9187
The ________ is the probability that the inventory available during lead time will meet
demand.
A) service level
B) inventory level
C) reorder point
D) maximum inventory level
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
The maximax strategy is:
A) Buy.
B) Rent.
C) Lease.
D) Brisk.
Which of these statements about the sensitivity report for the constraints is best?
A) Only $940 of the advertising budget is being spent on this campaign.
B) The advertising campaign needs another $2,560 to reach the maximum number of
customers.
C) It is possible to reach enough customers by spending only $60.
D) For every $1 increase in the budget, the ad campaign can reach twelve more
customers.
Taco Quatro
Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients,
cheese, meat, beans and tortillas.
A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla
needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2
ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the
Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa
sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new
Burritaco sells for $4.
The assistant manager checks the cooler one fine Monday morning and sees that they
have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas
on hand.
What is an appropriate constraint for this fast food vignette?
A) 250T + 400B + 150M + 400C
B) 4C + 1M + 0B + 4T ≤ 4
C) 2N + 4B + 4Q + 3E ≤ 400
D) 75N + 4B + 2Q + 3E
Cold & Calculating
The cold, calculating father did exactly that when examining the 27 year old failure to
launch man child that had turned his walk in closet into a bedroom. As he saw it, there
were five alternatives; each had its advantages and disadvantages, and under different
circumstances, each had a different financial incentive. He laid it all out neatly in a
table, but as not to arouse suspicion, he left the table’s labels very generic, so the
alternatives were simply labeled A through E while the different circumstances were
simply numbered one through three. He flicked the gray ash off of his favorite purple
smoking jacket and pondered the best course of action under each possible future. It
was good to be devious, he decided.
He set the analysis aside for a few days and had forgotten about it completely until one
night when his frequent dining companion Leonid Hurwicz visited his house and retired
to the drawing room for an apertif. “What you must do, my friend,” Hurwicz began, “is
to declare your coefficient of optimism, which can be tricky.” After forty-five minutes
of intense concentration, the cold, calculating father decided that his coefficient of
optimism was 0.5. What is the optimal choice for him?
A) A
B) B
C) C
D) D
Armed only with his fingers, the owner decides that the safest forecasting approach is a
weighted moving average using 0.6, 0.3, and 1 for the most recent three. Generate a
forecast for the year using this technique and then calculate forecast errors using MSE.
What is the mean squared error for this forecasting approach?
A) 5033
B) 3960
C) 4036
D) 3466
Which of the following is an equation or an inequality that expresses a resource
restriction in a mathematical model?
A) a decision variable
B) an objective function
C) a constraint
D) a parameter
Taco Quatro
Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients,
cheese, meat, beans and tortillas.
A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla
needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2
ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the
Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa
sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new
Burritaco sells for $4.
The assistant manager checks the cooler one fine Monday morning and sees that they
have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas
on hand.
What is an appropriate objective function for this fast food vignette?
A) Max Z = 2.75N + 4B + 2Q + 3E
B) Min Z = 400C + 150M + 400B + 250T
C) Min Z = 2.75N + 4B + 2Q + 3E
D) Max Z = 400C + 150M + 400B + 250T
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest
project and recorded them using different colors of sand on a pristine slab of white
marble. She used red for late start and late finish times and green for early start and
early finish times. Activity durations and their identifiers were written with black sand.
She finished her task and had an opportunity to admire her work only briefly before a
colleague came by and swept most of it away. Sadly, this was before Carrie could
record the numbers on a more permanent medium, so now she turns to you to help.
What is the early finish time for activity K?
A) 36
B) 35
C) 34
D) 33
If order quantity is increased, annual holding cost ________, annual order cost
________, and change in annual total cost ________.
A) decreases, increases, is positive
B) decreases, increases, cannot be determined
C) increases, decreases, is negative
D) increases, decreases, cannot be determined
Which of the statements about this portion of the sensitivity report is best?
A) Cheese costs more than meat.
B) One additional pound of meat should be purchased if it can be acquired for $2 or
less.
C) There is both cheese and meat left over if the optimal product mix is produced.
D) The shadow price of cheese can rise to 16.8167 before the right hand side changes.
________ demand items are final products demanded by an external customer.
A) Dependent
B) Independent
C) External
D) Integrated
Larry’s Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for
$3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than
$160. The objective function that minimizes these costs for Larry is:
A) 5S + 3.5W ≤ 160.
B) Min 5S + 3.5 W.
C) Max 5S + 3.5 W.
D) Min 5S + 3.5W ≥ 160.
A crew of mechanics at the Department of Transportation garage make minor repairs to
snowplows during the winter. The snowplows break down at an average rate of 4
vehicles per day and breakdowns are distributed according to the Poisson distribution.
The mechanic can service an average of 7 vehicles per day with a repair time
distribution that approximates a negative exponential distribution. Assume an 8 hour
day.
In a single-server queuing system, if 12 customers arrive per hour and 30 customers are
served per hour, what is the probability that there are no customers in the system?
A) 0.75
B) 0.60
C) 0.40
D) 0.25
Assignments are made to locations with ________ in the opportunity cost table.
A) -1 or 1
B) -1
C) 1
D) 0
The following data represents quarterly sales of lawnmowers.
The manager of “Skis 4 U” is preparing a forecast for February of 2010. Demand
exhibits both trend and seasonality. The trend equation for monthly demand is y = 4375
+ 80t, wheret = 1 for January 2009. The seasonal index for February is 1.25. The
forecast for February is:
A) 4575
B) 4583
C) 5668
D) 6769
Two hundred simulation runs were completed using the probability of a machine
breakdown from the table below. The average number of breakdowns from the
simulation trials was 1.93 with a standard deviation of 0.20.
What is the probability of 2 or fewer breakdowns?
A) .25
B) .35
C) .36
D) .71
Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would
the forecast for the next period be using simple exponential smoothing?
A) 36.9
B) 57.5
C) 60.5
D) 62.5
The term opportunity loss is most closely related to:
A) maximin regret.
B) maximax regret.
C) minimax regret.
D) minimin regret.
A professor needs help from three student helpers to complete four tasks. The first task
is grading; the second is scanning; the third is copying, and the fourth is organizing
student portfolios. The estimated time for each student to do each task is given in the
matrix below.
How many tasks will be assigned to the students?
A) 2 tasks
B) 3 tasks
C) 4 tasks
D) none, because the students take too long
Use the following table and the information to answer the questions below.
In the following transportation matrix, all cells except 2C have been evaluated and
show no improvement. Evaluate that cell.
Make the necessary allocation to cell 2C and determine the total transportation cost.
A) 936
B) 928
C) 908
D) 852
E) 878
Consider the following objective function and constraint: C(x) = 2x1
2 – 15x + 3x2
3 – 9x2
+ 30, such that x1 = 3x2. Which of the following is the correct Lagrangian function?
A) L = 2x1
2 – 15x + 3x2
3 – 9x2 + 30 – λ (3x2 – x1)
B) L = 2x1
2 – 15x + 3x2
3 – 9x2 + 30 – λ (x2 – 3x1)
C) L = 2x1
2 – 15x + 3x2
3 – 9x2 + 30 – λ (3x1 – x2)
D) L = 2x1
2 – 15x + 3x2
3 – 9x2 + 30 – λ (3x2 – 3x1)
An optimization problem that has multiple optimal solutions:
A) means that there are actually no optimal solutions.
B) is reflected by the entire feasible region being optimal
C) means that the surplus for a third constraint cannot be calculated.
D) provides the decision-maker with increased flexibility.
Kushie’s Coffee in Bangalore is a quaint establishment nestled near MG Road in the
central business district. It serves coffee and fruit cake to a clientele that has been
enjoying these products for over fifty years. The demand for coffee beans is 6600 cases
per year (each case has 24 ten-pound bags). It would be disastrous for them to run out
of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5
per case to order coffee. As coffee is a perishable product, the holding cost is fairly high
at $40/case/year. The lead time to receive an order is seven days. Kushie’s is open 300
days a year.
Assumptions of the EOQ model include:
A) Demand is normally distributed.
B) Lead time is normally distributed.
C) There is instantaneous order receipt.
D) Backorders can occur.
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
A) trend only
B) trend plus seasonal
C) trend plus random
D) none of the above
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.
If choice A is strongly preferred to choice B and choice B is moderately preferred to
choice C, and the decision maker says choice C is equally preferred to choice A, what
conclusion can be drawn?
A) The decision maker is consistent.
B) The decision maker is inconsistent.
C) The pairwise comparison matrix is symmetric.
D) The decision maker has already synthesized.
A succession of events that do not affect each other are ________.
Given the following data, compute the MAD for the forecast.
Year Demand Forecast
In a pure strategy game the optimal strategy for each player results in the same payoff,
called an ________ point.
What special case of linear programming should be used to model this situation?
In using the Vogel’s Approximation model, a ________ is the XOAXOAerence between
the largest and next largest cell cost in a row.
The ________ test is a statistical test to see if an observed data fit a particular
probability distribution.
Refer to the table below to answer the question(s) that follow:
What are the estimated standard deviations (in weeks) in the times for activities A-H?
Given the following payoff/loss table for a mixed strategy game between two players:
Identify dominated strategy(s), if it (they) exist(s).
Solve the following integer linear program:
MAX + 2 +
subject to: 7 + 4 + 3 ≤ 28
, , ≥ 0
, integer
Use the following table to answer the question(s) below.
What decision should be made by the conservative decision maker?
The shortest route problem formulation requires a statement that mandates that what
goes in to a node must equal what comes out of that node. This is referred to as
________.
Kushie’s Coffee in Bangalore is a quaint establishment nestled near MG Road in the
central business district. It serves coffee and fruit cake to a clientele that has been
enjoying these products for over fifty years. The demand for coffee beans is 6600 cases
per year (each case has 24 ten-pound bags). It would be disastrous for them to run out
of coffee, so they keep a safety stock of 30 cases. The cases cost $4800 and it costs $5
per case to order coffee. As coffee is a perishable product, the holding cost is fairly high
at $40/case/year. The lead time to receive an order is seven days. Kushie’s is open 300
days a year.
How many orders per year does Kushie’s place if they order a cost minimizing
quantity?
The following data summarizes the historical demand for a product:
A manager uses the following equation to predict monthly receipts: Yt = 4,000 + 30t.
What is the forecast for July of next year if t = 0 in April of this year?
A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The
per unit contribution for the juice glasses (x1) is equal to 60 – 5x1, and the per unit
contribution for the cocktail glasses (x2) is 80 – 4x2 for a total contribution of 60x1 –
5x1
2 + 80x2 – 4x2
2. Demand requires that the production of juice glasses is twice the
production of cocktail glasses.(x1 = 2x2). What is the Lagrangian function for this
problem?
L = 60x1 – 5x1
Given the following data on the number of pints of ice cream sold at a local ice cream
store for a 6-period time frame:
Compute a 3-period moving average for period 7.