Experiments with repeated independent trials will be described by the binomial
distribution if:
A) each trial result influences the next.
B) each trial has exactly two outcomes whose probabilities do not change.
C) the trials are continuous.
D) the time between trials is constant.
What is the vacation of choice under the minimax regret criterion?
A) Galapagos Islands
B) Eastern Europe
C) Southeast Asia
D) Australia
Donuts Please
The number of donuts needed for department meetings at the start of the semester can
be modeled by the continuous probability distribution , which we can integrate
from 0 to some value x, which is the number of days before the actual beginning of the
semester.
What is the value for x when random number r is equal to ten?
A) 18.09
B) 52.59
C) 146.41
D) 401.43
A keyboard costs $1000, and the annual holding cost is 25%. Annual demand is 10,000
units, and the order cost is $150 per order. What is the approximate economic order
quantity?
A) 16
B) 70
C) 110
D) 183
In a linear programming problem, the binding constraints for the optimal solution are:
5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
A) 2x1 + 1x2
B) 7x1 + 8x2
C) 80x1 + 60x2
D) 25x1 + 15x2
Given an EOQ model with shortages in which annual demand is 4200 units, Co = $160,
Cc = $7 per unit per year, and Cs = $25, what is the order quantity?
A) 394.72
B) 495.74
C) 296.51
D) 456.34
For the following frequency distribution of demand, the random number 23 would be
interpreted as a demand of:
A) 0
B) 1
C) 2
D) 3
A limitation of simulation is that:
A) models are typically well-structured and must be developed for problems that are
also well-structured.
B) it is usually possible to realistically validate simulation results.
C) model building is costly and time-consuming.
D) it is more Difficult to manipulate the elements of a computer simulation than the
actual system.
The probability of independent events occurring in succession is computed by
________ the probabilities of each event.
A) multiplying
B) adding
C) subtracting
D) dividing
Assume that it takes a college student an average of 5 minutes to find a parking spot in
the main parking lot. Assume also that this time is normally distributed with a standard
deviation of 2 minutes. Find the probability that a randomly selected college student
will take between 2 and 6 minutes to find a parking spot in the main parking lot.
A) 0.1950
B) 0.4772
C) 0.4332
D) 0.6247
Consider the following frequency of demand and random numbers:
Random numbers: 0.13, 0.81, 0.53.
If the simulation begins with the third random number, the simulated value for demand
would be:
A) 0
B) 1
C) 2
D) 3
E) 4
The transition matrix below shows the probabilities that customer switch between two
grocery stores, Don’s and Limmer’s, each week.
The ________ is average, constant probability that the system will be in a state in the
future.
A) transition probability
B) state of the system
C) steady-state probability
D) transition matrix
Yowzah Bids
Yowzah receives bids from four companies we’ll call A, B, C, and D to supply product
for the coming year. Renee DeCartes, the Yowzah VP of Plotting takes the bids and
creates this graph to bring to the next executive meeting.
The company with the highest variable cost is:
A) A.
B) B.
C) C.
D) D.
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.Determine the average time that a snowplow is out of service.
A) .33 hours
B) 20 minutes
C) 2.64 hours
D) .19 days
In the basic EOQ model, if D = 60 per month, Co = $12, and Cc = $10 per unit per
month, what is the EOQ?
A) 11
B) 12
C) 13
D) 14
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
percentage of the time is the system completely empty?
A) 9%
B) 13%
C) 17%
D) 21%
In a(n) ________ inventory system, a constant amount is ordered when inventory
declines to a predetermined level.
A) optimal
B) economic
C) periodic
D) continuous
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has
a limited amount of the three ingredients used to produce these chips available for his
next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of
herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of
herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of
flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of
vinegar chips $0.50.For the production combination of 800 bags of lime and 600 bags
of vinegar, which of the three resources is (are) not completely used?
A) flour only
B) salt only
C) herbs only
D) salt and flour
Employees of a local company are classified according to gender and job type. The
following table summarizes the number of people in each job category.
Male (M) Female (F)JobAdministrative (AD) 110 10
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
If an employee is selected at random, what is the probability that the employee is
female or works as a member of the administration?
A) .17
B) .67
C) .70
D) .73
The Vacation
Final exams are almost here and once they are done, it will be time to reward myself
with a well-deserved vacation. As a state employee, I haven’t seen a raise since… well,
ever. Thus an important criterion, in fact the most important criterion is to find an exotic
region that can be visited inexpensively. There are three states of nature that could
impact costs in these five areas of interest, and they correspond to the relative strength
of the US Dollar against that region’s dominant currency. Rather than squander my time
doing any actual publishable research, instead I have determined the average cost per
day to visit each region under each of the possible states of nature. This table, which
should not be construed as actual vacation advice, appears below.
An optimistic vacationer would opt for:
A) Scandinavia.
B) Galapagos Islands.
C) Australia.
D) Eastern Europe.
In the basic EOQ model, if annual demand is 50, carrying cost is $2 per unit per year,
and ordering cost is $15, what is the EOQ?
A) 27.39
B) 26.39
C) 25.39
D) 24.39
Which of the following could not be a linear programming problem constraint?
A) 1A + 2B ≠ 3
B) 1A + 2B = 3
C) 1A + 2B ≤ 3
D) 1A + 2B ≥ 3
A single-bay car wash with a Poisson arrival rate and an exponential service time has
cars arriving at an average of 10 minutes apart with an average service time of 4
minutes. What is the system utilization?
A) 0.3
B) 0.4
C) 0.5
D) 0.6
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.
What is the average number of folks either purchasing a soda or waiting to purchase
one?
A) 1.83
B) 2.16
C) 2.46
D) 2.92
In an EOQ model, as the carrying cost increases, the order quantity:
A) increases.
B) decreases.
C) remains the same.
D) cannot be determined.
In a linear programming problem, a valid objective function can be represented as:
A) Max Z = 5xy
B) Max Z 5x2 + 2y2
C) Max 3x + 3y + 1/3 z
D) Min (x1 + x2) / x3
The region that satisfies all of the constraints in a graphical linear programming
problem is called the:
A) region of optimality.
B) feasible solution space.
C) region of non-negativity.
D) optimal solution space.
A bakery is considering hiring another clerk to better serve customers. To help with this
decision, records were kept to determine how many customers arrived in 10-minute
intervals. Based on 100 10-minute intervals, the following probability distribution and
random number assignments developed.
Suppose the next three random numbers were .18, .89 and .67. How many customers
would have arrived during this 30-minute period?
A) 22
B) 23
C) 24
D) 25
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.
“Regrets? I’ve had a few,” and his voice trailed off. He was speaking to no one in
particular, which he found himself doing with alarming frequency. If at all possible, he
made decisions that would allow him to look back with as little regret as possible.
Which alternative would be the best choice given this proclivity for minimizing regret?
A) A
B) B
C) C
D) D
As service level increases, expected number of stockouts ________ and safety stock
________.
A) increase, increases
B) decrease, decreases
C) decrease, increases
D) increase, decreases
Companies A, B, and C supply components to three plants (F, G, and H) via two
crossdocking facilities (D and E). It costs $4 to ship from D regardless of final
destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C
costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and
$8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively
and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D
and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin,
had previously used “Chain of Fools” as her supply chain consulting company, but now
turns to you for some solid advice.
Write every constraint that involves Company A.
The minimax regret criterion:
A) maximizes the minimum regret.
B) minimizes the minimum regret.
C) minimizes the maximum regret.
D) maximizes the maximum regret.
A key component of business analytics is the recent availability of large amounts of
data.
A company distributes repair parts for high-end appliances. The annual demand is
81,000 and the company operates 300 days per year. The annual carrying cost is 20% of
the item cost, which is $500. The ordering cost is estimated at $60 and the shortage cost
is $150.
If the daily demand is 25 and the lead time in days is 4, what is the reorder point?
The best feasible solution is ________.
A linear programming model solution with no integer restrictions is called a ________
solution.
A life insurance company wants to estimate its annual payouts. Assume that the
probability distribution of the lifetimes of the participants is approximately a normal
distribution with a mean of 68 years and a standard deviation of 4 years. What
proportion of the participants die before they reach the age of 65?
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 constraint for the transshipment node in Knoxville?
The diagram below shows the activities on the nodes, and the table shows the normal
time and crash time (in days) and cost for each activity.
Determine which activities should be crashed to shorten the project by 1 day.
In a binomial distribution process, there are ________ possible outcomes.
In a network flow problem, ________ connect nodes and show flow from one point to
another.
When the earliest start time (ES) of an activity is subtracted from the latest start time
(LS) of an activity, the value obtained is called ________.
Refer to the table below to answer the question(s) that follow:
What are the estimated slack times (in weeks) for activities A-H?
The diagram below shows the activities on the nodes, and the table shows the normal
time and crash time (in days) and cost for each activity.
Determine which activities should be crashed to shorten the project by 2 days.
Developing the ________ probability distribution helps to determine random number
ranges.
The student internship director needs as much coverage as possible in the office next
week. The more hours that can be put in each day, the better. She has asked the students
to provide a list of how many hours they are available each day of the week. Each
student can be there on only one day and there must be a student in the office each day
of the week. Use the table below and the tables provided to determine the schedule that
gives the most coverage. Note that the objective of this problem is to maximize the
hours worked, not minimize.
In setting up the an intermediate (transshipment) node constraint, assume that there are
three sources, two intermediate nodes, and two destinations, and travel is possible
between all sources and the intermediate nodes and between all intermediate nodes and
all destinations for a given transshipment problem. In addition, assume that no travel is
possible between source nodes, between intermediate nodes, and between destination
nodes, and no direct travel from source nodes to destination nodes. Let the source nodes
be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination
nodes be labeled as 6 and 7.
If there are 300 units available at source 2, state the constraint for source node 2.
SS 1 21 100 5 62 200 4 23 150 3 64 50 9 7DD 250 250What is the objective function?
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 2Student score 84 75Mean 75 60
Standard deviation 7 8
Which student scored better compared to the rest of their section?