In a given experiment the probabilities of mutually exclusive events sum to:
A) o
B) 0.5
C) 1
D) This cannot be answered without knowing the probability values of the events.
The ________ criterion results in the maximum of the minimum payoffs.
A) minimax
B) maximax
C) maximin
D) minimin
Decision analysis is a ________ technique.
A) linear mathematical programming
B) probabilistic
C) network
D) non-linear programming technique
Atwitter
The college director of global activities was hopeful that the print ads in the school
newspaper and 30 second spots on the campus radio station would spur some interest in
the array of study tour and study abroad options he had secured. The communications
director for the college had other ideas; she favored a social media campaign consisting
of tweets and facebook postings. “This is the most ridiculous thing I ever heard of,” he
whined to the dean.
The communications director’s market research revealed the following:
The advertising budget is $3500, but there is no requirement that all the money be spent.
The newspaper has only four issues before the end of the semester, but the radio is a 24/7
operation and has two dozen 30 second slots available. Facebook postings must be
alternated with the rest of the mindless drivel posted on the college page; thus there is
space for only three postings before the end of the semester. Twitter is complicated by the
140 character requirement. The communications director feels she needs five tweets to
convey a single message about tours and semesters abroad, so for one message, the cost
would be $25 for each of the five components of the single ad. Due to thumb fatigue, she
feels that she has only 2800 characters left in her thumbs before the end of the semester. (A
side note – During the intersession period, she plans to embark on a strict regimen of
thumb yoga to prepare for the coming semester.) Which of these is an appropriate
constraint for this scenario?
A) 5,000N + 3,000R + 700T + 200F ≤ 3,500
B) 500N + 250R + 125T + 15F ≤ 3,500
C) N + R + T + F ≥ 36
D) T ≤ 2,800
If the probability of an event is 0.36, what random number range specifies this
properly?
A) 0.10 – 0.20
B) 0.20 – 0.30
C) 0.30 – 0.40
D) 0.40 – 0.50
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.
What is the increase in their EOQ if all of the model parameters (except the number of
days in a year) double?
A) 100%
B) 33%
C) 41%
D) 50%
A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost
niched product while meeting the dietary guidelines for protein and sodium. Once the
model has been run, the surplus variable in the sodium constraint has a value of 1300
milligrams. The best interpretation of this outcome is:
A) The value of the sodium in a hot dog is 1300.
B) The amount of sodium in a single hot dog should be 1300 milligrams.
C) The minimum cost hot dog has 1300 milligrams more sodium than required.
D) A hot dog should have at least 1300 milligrams of sodium.
Simulations are normally done:
A) manually.
B) in a casino.
C) by a spreadsheet.
D) on the computer.
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
Which of the following possible values of alpha would cause exponential smoothing to
respond the most slowly to sudden changes in forecast errors?
A) .01
B) .50
C) .90
D) 3.14
Dinnertime
A professor is planning an informal gathering for 100 or so of his closest friends. The
project breaks down as follows:
What is the slack time for the Stock wine cellar activity?
A) 8
B) 10
C) 12
D) 14
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.
Which of the following are assumptions or requirements of transportation problems?
I. Goods are the same from each source.
II. There must be a single source.
III. Minimum quantities must be shipped.
IV. Shipping costs per unit do not vary with the quantity shipped.
A) I and III
B) I, II, and IV
C) I and IV
D) II and III
A Markov assumption is that the probabilities in each row sum to 1 because they are:
A) mutually exclusive.
B) collectively exhaustive.
C) mutually exclusive and collectively exhaustive.
D) mutually exclusive or collectively exhaustive.
After plowing through contracts for a decade, the contract writer knew about how long
it took to crank out the material necessary to satisfy a contract’s requirements. The
distribution could be modeled using the data provided in this table.
Using the random number table 14.3 in your text, column 1, reading across row 3, what
is the standard deviation of the average length of the next five contracts?
A) 0.75
B) 0.70
C) 0.65
D) 0.60
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. “Wait a minute Hurwicz, that figure sounds as if I’m afraid of
making a decision,” the father intoned. “It seems that depending on how optimistic I
am, the optimal choice changes between alternative B and alternative D.” What
coefficient of optimism would make the cold, calculating father indifferent between
these two alternatives?
A) 583
B) 616
C) 666
D) 714
In adjusted exponential smoothing, the closer beta is to ________, the stronger a trend
is reflected.
A) -1 or 1
B) -1
C) 0
D) 1
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.
The supplier offers the Krewe of Orpheus a deal; if they will buy at least 50,001 at a
time, they will pay only 4 cents each, and if they buy at least 100,001 at a time, they
will pay only 3 cents each. What is the optimal order quantity?
A) 41,892
B) 46,837
C) 50,001
D) 100,001
Determining the worst payoff for each alternative and choosing the alternative with the
best of the worst payoffs is called a ________ criterion.
A) maximin
B) minimin
C) maximax
D) minimax
The theoretical limit on the number of constraints that can be handled by a linear
programming problem is:
A) 2
B)3
C)4
D) unlimited.
Balanced transportation problems have which of the following type of constraints?
A) ≥
B) ≤
C) =
D) <
A single-server waiting line system has an arrival pattern characterized by a Poisson
distribution with 3 customers per hour. The average service time is 12 minutes. The
service times are distributed according to the negative exponential distribution.The
average time a customer can expect to wait in line is:
A) 18 minutes.
B) 36 minutes.
C) 30 minutes.
D) 60 minutes.
The ________ is the offensive player’s gain and the defensive player’s loss in a
zero-sum game.
A) game situation
B) value of the game
C) strategy
D) best strategy
E) pure strategy
Semester Prep
The department chair reviewed last year’s schedule, the degree requirements for the
ever popular Operations and Supply Chain major, and the emails that had drifted into
her mailbox over the last week. Naturally, every professor in the department had his
own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all
costs. In an effort to placate the senior faculty members of the department, the chair
sent an email asking them to supply the prep time for each of the classes they were
qualified to teach, promising to assign them the least taxing schedule possible. Each of
her department members had to teach at least two courses, but no more than three. The
elective courses, Project Management, Quality Management, Control and Planning,
Logistics, and Management Science each had to be offered once and the department
needed to offer at least six sections of the Introduction to Operations class. The prep
times each professor estimated for each course appear in the table below.
Copied below is a portion of the answer report that shows the constraints related to the
faculty assignment. Which of these statements is best according to the answer report?
A) Geoff is assigned to teach Introduction to Operations.
B) Tim is assigned to teach two courses.
C) David is assigned to teach Management Science.
D) Saba is assigned to teach two courses.
Consider the following network representation of shipment routes between plants, a
distribution center, and retail outlets. The numbers next to the arcs represent shipping
costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to
$2.
Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail
outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
In an assignment problem all supply and demand values equal are:
A) 0
B) 1
C) 2
D) greater than 1.
At Joe’s Pool Hall they rent tables by the hour and also rent Balabushka pool cues for
purists that can’t afford their own. The rental process for these cues is exhaustive and
takes an hour and a half for each application. There are three leasing agents that conduct
these interviews, and on average, it is one hour between customer arrivals.What is the
average time a customer spends in the system?
A) 2.5 minutes
B) 3.7 minutes
C) 4.3 minutes
D) 5.6 minutes
At the initial basic feasible solution at the origin, only slack variables have a value
greater than:
A) 0
B) 1
C) -1
D) 1 or -1
The Lagrange multiplier reflects the appropriate change in the objective function
resulting from a unit change in the ________ of the constraint equation.
A) coefficient
B) objective function
C) right-hand side
D) shadow price
Assume that a plant manager has to decide where to locate its warehouse The decision
has been narrowed down to choices among the following three cities: Detroit,
Cleveland, and St. Louis. The company has weighted each of these criteria in terms of
its relative importance in the decision making process, and it has analyzed each
potential warehouse location and graded them according to each criteria as shown in the
following table.
From the scores for each location, determine where the warehouse should be located.
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred.
Which variable is not a component of break-even analysis?
A) fixed costs
B) variable costs
C) number of employees
D) number of customers
The expected value of sample information:
A) is never more than EVPI.
B) can be greater or less than EVPI.
C) can be positive or negative.
D) is equivalent to the EVPI.
Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M).
Each big shelf costs $500 and requires 100 cubic feet of storage space, and each
medium shelf costs $300 and requires 90 cubic feet of storage space. The company has
$75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet
available for storage. Profit for each big shelf is $300 and for each medium shelf is
$150. What is the maximum profit?
A) $35,000
B) $45,000
C) $55,000
D) $65,000
Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M).
Each big shelf costs $500 and requires 100 cubic feet of storage space, and each
medium shelf costs $300 and requires 90 cubic feet of storage space. The company has
$75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet
available for storage. Profit for each big shelf is $300 and for each medium shelf is
$150. In order to maximize profit, how many big shelves (B) and how many medium
shelves (M) should be purchased?
A) B = 90, M = 75
B) B = 150, M = 0
C) B = 0, M = 200
D) B = 100, M = 100
Consider the following decision tree.
What is the value associated with node 3?
In the basic EOQ model, the amount ordered is received in ________ shipment(s).
The local grocery store consists of two cashiers. The customers arrive according to a
Poisson distribution and the service times are based on a negative exponential
distribution. The average customer service time is 5 minutes and the average time
between the arrivals of successive customers is 3 minutes. What is the probability that
there are no customers in the grocery store?
To determine the sensitivity range for the coefficient of a variable in the objective
function, calculations are performed such that all values in the cj– zj row are ________.
An investor has $80,000 to invest in three stocks, stock A costs $100, stock B costs
$120 and stock C costs $80. Each stock A has a risk factor of 8, each stock B has a risk
factor of 10 and each stock C has a risk factor of 7. The investor believes that the sum
of the risk factors for all stocks purchase should not exceed 6000. The projected annual
growth rate for the three stocks are 9%, 13% and 8% respectively. The projected annual
dividend income from these stocks are as follows: Stock A: $14/stock, Stock B:
$15/stock, and Stock C: $20/stock. The investor desires an annual dividend income of
$10,000. The investor has established the following goals in order of their importance:
(1) The investor believes that the budget cannot be exceeded. (d1)(2) The risk factor
should not exceed the target amount of 6000. (d2)(3) The average annual growth rate in
stock prices must be at least 10%. (d3)(4) The investor desires a dividend income of at
least $10,000. (d4)
State the goal programming objective function.
Solve the following integer linear program:
MAX +
subject to: 4 + 6 ≤ 22
+ 5 ≤ 15
2 + ≤ 9
, x ≥ 0, integer
A single-bay car wash with a Poisson arrival rate and an exponential service time has
cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a
car. What is the system utilization?
A(n) ________ table is developed by first subtracting the minimum value in each row
from all other row values and then repeating the process for each column.
If only one of three events can occur at any given time, the events are ________.
The quality control manager for ENTA Inc. must decide whether to accept (A1), further
analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff
table is available. Historical data indicates that there is 30% chance that the lot is poor
quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is
good quality (S3).
What is the maximum amount that you would be willing to pay for perfect information?
Given the following data on hotel check-ins for a 6-month period:
July: 70 rooms
August: 105 rooms
September: 90 rooms
October: 120 rooms
November: 110 rooms
December: 115 rooms
Using a 3-month moving average, how many check-ins can be forecasted for January?
Madlantic Devices designs and manufactures high-end medical devices. The facilities
in Madison and Atlanta serve as design and component manufacturing facilities.
Components are then shipped to warehouses in Philadelphia or Knoxville, where they
are held until final assembly is completed at either Dayton, Bloomington, or Albany.
Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton,
Bloomington, and Albany is 450, 500, and 610, respectively.
The network representing the shipping routs is shown below.
The costs for shipping between each facility is shown below. A blank cell indicates that
shipping between two facilities is not permitted.
What is the objective function for this problem? Use the notation Xij, where i and j
correspond to the node numbers indicated in the diagram.
Given the following data on hotel check-ins for a 6-month period:
July: 70 rooms
August: 105 rooms
September: 90 rooms
October: 120 rooms
November: 110 rooms
December: 115 rooms
Using the exponential smoothing factor 0.3, how many check-ins can be forecasted for
January? Assume the forecast for December was 122 rooms.
Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102,
101, 96, 95, 90 and 92. Develop a forecast for today using a 2-day moving average.
If a firm’s profit is Z = 20p -2p2 + 40, then the optimal value of I yields a maximum
profit of ________.
An ________ solution is reached when a feasible integer solution is reached at a node
that has an upper bound equal to lower bound.
Due to increased sales, a company is considering building three new distribution centers
(DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in
thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The
cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of
operating at each location is the same, and therefore not a consideration in making the
location decision.
The table below shows the cost ($ per item) for shipping from each DC to each region.
Region
The demand for region A is 70,000 units; for region B, 100,000 units; for region C,
50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the
distribution center will be 500,000 units.
Define the decision variables for this situation.
The objective function formulation for a goal programming model is as follows:
Min P1d1
–, P2d2
–, P3d1
+, P4d3
–
Which one of the variables would the program designers like to have as the second goal
such that its deviation from zero is minimized?
d2
If a firm’s profit is Z = 100p-8p2 +16, then the maximum profit occurs where p =
________.
In the ________ queuing system, which is a variation of the single-phase single-channel
model, the service rate does not have to exceed the arrival rate.