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An automotive center keeps tracks of customer complaints received each week. The
probability distribution for complaints can be represented as the table shown below. The
random variable xi represents the number of complaints, and p(xi) is the probability of
receiving xi complaints.
What is the average number of complaints received per week?
A) 12
B) 32
C) 12
D) 83
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 average length of the next five contracts?
A) 4.6
B) 4.8
C) 5.0
D) 5.2
________ is a category of statistical techniques that uses historical data to predict future
behavior.
A) Qualitative methods
B) Regression
C) Time series
D) Quantitative methods
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.
Which of these constraints allows for some inventory to be held at one of the crossdock
facilities?
A) AD + BD + CD - DF - DG - DH ≥ 0
B) AD + BD + CD - DF - DG - DH = 600
C) AD + BD + CD = DF - DG - DH = 600
D) AD + BD + CD + DF + DG + DH = 600
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
not be accepted at either university?
A) .30
B) .36
C) .44
D) .56
A retired operations management professor moves to New Orleans, joins the Krewe of
Orpheus and convinces krewe leadership to buy their own swizzle stick production
equipment. They invest in a medium-scale machine called the Swizzo 2025, which is
capable of producing swizzle sticks at the rate of 1800 per day. What is the optimal
batch size?
A) 126,548
B) 99,856
C) 74,268
D) 56,593
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.
Which constraint represents the quantity shipped to retail outlet 6?
A) X23 + X36 = 450
B) X23 + X36 + X26 = 450
C) X36 + X26 ≤ 450
D) X36 + X26 = 450
E) 3X36 + 5X26 = 450
The advantage of a Gantt chart over other charts is its:
A) feasibility.
B) practicality.
C) simplicity.
D) linearity.
Project management differs from management of more traditional day-to-day activities
because:
A) it has limited time frame.
B) it has an unlimited budget.
C) it is more expensive.
D) it involves more of the workforce.
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of
stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The
investor has up to $50,000 to invest.
An appropriate part of the model would be:
A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000.
B) MAX 15X1 + 47.25X2 + 110X3.
C) X1 + X2 +X3 ≤ 50,000.
D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3.
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.
In the Monte Carlo process, values for a random variable are generated by ________ a
probability distribution.
A) sampling from
B) running
C) integrating
D) implementing
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.How many
customers are either waiting or being served on average?
A) 1.5
B) 1.74
C) 1.98
D) 2.22
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.
What is the reduced cost if we decide to allocate to cell 2C?
A) -2
B) -1
C) 0
D) +1
E) +2
The ________ minimizes the maximum regret.
A) maximax regret criterion
B) minimax regret criterion
C) minimin regret criterion
D) maximin regret criterion
The maximin approach to decision making refers to:
A) minimizing the maximum return.
B) maximizing the minimum return.
C) maximizing the maximum return.
D) minimizing the minimum return.
Which of these decision support systems is the most comprehensive with respect to an
entire organization?
A) an Excel spreadsheet
B) an ERP
C) QM for Windows
D) OLAP
The Lagrangian function is differentiated with respect to each variable, and the
resulting equations are solved:
A) in the order of the variables.
B) one after the other.
C) one at a time.
D) simultaneously.
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.On average, how long does a plow wait before the mechanic begins the repair?
A) 0.19 hour
B) 1.25 hours
C) 1.52 hours
D) 2.64 hours
Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).
Which is the appropriate objective function for this scenario?
A) minimize P1d1
+,P2d2
--,P3d3
+,P4d4
+
B) maximize Z = $16R + $24W
C) maximize Z = $8R + $12W
D) maximize P1d1
-,P2d2
+-,P3d3
-,P4d4
-
In a transportation problem, items are allocated from sources to destinations at a:
A) maximum cost.
B) minimum cost.
C) minimum profit.
D) minimum revenue.
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. Use this portion of the sensitivity report to evaluate the following
statements:
A) The noise level around the farm should be over 60 decibels.
B) The fertilizer generated will be 160 ounces per week.
C) Layer pellets will be consumed at the rate of 96 ounces per week.
D) The plumage score will be less than 40.
A rendering plant wishes to use the data (sales records from a few local businesses and
the month of the year) to help determine their supply level for the coming months. The
records shown in the table provide an excellent opportunity for you to assist them with
their forecasting.
What is the forecast for July if exponential smoothing with an alpha=.04 generated a
forecast of 43.0 for June?
A) 41.25
B) 40.64
C) 43.16
D) 42.88
In ________ additional information is used to alter the marginal probability of the
occurrence of an event.
A) Bayesian analysis
B) decision analysis
C) probability analysis
D) decision making under certainty
Mondo's Runway Show
Mondo Guerra is matching his models with his latest collection for Fashion Week. He
has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest
designs run the gamut from prt--porter to an evening gown and he'd like to make sure
each outfit looks as good as possible by having it worn on the runway by the right
model. After an anxious month of sewing, he has each model try on each outfit and he
assigns a fabulosity score to each combination as indicated in the table.
What is the best overall fabulosity score that Mondo can hope for?
A) 9
B) 25
C) 36
D) 45
People who take a chance on a bonanza with a very low probability of occurrence in
lieu of a sure thing are:
A) risk takers.
B) risk averters.
C) risk calculators.
D) risk predictors.
Jolt - M
The soda machines outside the lecture hall sees a steady stream of customers
throughout the day. Between the student's use of the machine and the mechanism, it
takes 15 seconds (exponentially distributed) to deliver a can of carbonated sugar water
to a thirsty customer. Over the course of a twelve hour lecture day, students arrive at the
rate of 450 per hour.
What is the likelihood that there aren't enough customers making purchases or waiting
in line to form a barbershop quartet?
A) 0.33
B) 0.30
C) 0.25
D) 0.20
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.
About how many people are waiting in line at the machine on average?
A) 0
B) 1
C) 2
D) 3
Linear mathematical programming techniques assume that all parameters in the models
are:
A) known with certainty.
B) unknown.
C) predictable.
D) unpredictable.
William realizes he wasn't as ambitious as he should have been, and decides to
reformulate his model such that the second priority is income of $550. After pressing
"Solve" he reviews the sensitivity report shown below. Which statement is best?
A) William income has increased from $500 to $520.
B) William income cannot be determined from this report.
C) William can increase his profit beyond $550 is he would revise his profit constraint
again.
D) William's income has increased from $500 to $530.
The ________ method for solving nonlinear programming problems is referred to as
substitution.
A) least complex
B) most complex
C) most difficult
D) least difficult
The production manager for the Coory soft drink company is considering the
production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited
resources are 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 $3.00 per case and profits for diet soft drink are
$2.00 per case. What is the objective function?
A) MAX $2R + $4D
B) MAX $3R + $2D
C) MAX $3D + $2R
D) MAX $4D + $2R
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.
Calculate the scores for each location and state where the warehouse should be located.
Inventory ________ costs include transportation and inspection.
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 5-period moving average for period 6.
A newly opened bed-and-breakfast projects the following:
Monthly fixed costs $8000
Variable cost per occupied room per night $40
Revenue per occupied room per night $165
Write the expression for total revenue per month.
Figure Delivery Routes
Consider the network diagram given in Figure 1. Assume that the amount on each
branch is the distance in miles between the respective nodes. Also assume that it is not
possible to travel from a node with a higher number to a node with a lower number.
Write the constraint associated with the second node (node 2) for the 0-1 integer linear
programming formulation of the shortest route problem.
A multiple optimal solution occurs when an empty cell has a cost change of ________
and all other empty cells are positive.
A ________ is a computer-based system that helps decision-makers address complex
problems that involve XOAXOAerent parts of an organization and operations.
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)Job
Administrative (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 male?
The standard deviation of the standard normal distribution is equal to ________.
A local gym has discovered that their demand for personal trainers (measured in hours)
is related not only to their own advertising expenditures in the prior month, but also to
the demand for doughnuts and swim gear in the prior month at neighboring stores. The
gym has developed the following regression model to forecast demand for personal
trainers:
Demand = 185 + (0.15 advertising expenditures) - (0.05 doughnuts) + (0.23 swim gear
sales)
What is the forecast for October, given advertising expenditures of 1000, doughnut
sales of 2450, and swim gear sales of 782 in September?
Solve the following problem using the simplex method.
Minimize Z = 3x1 + 4x2 + 8x3
Subject to: 2x1 + x2 ≥ 6
x2 + 2x3 ≥ 4
x1, x2 ≥ 0
A production of 300 units of Twiddle Bugs, an educational toy for children, must be
completed within 1 week by BugU Manufacturing. Two production lines are available,
each for 30 hours during the week. Production line 1 can produce five units per hour
and production line 2 can produce four units an hour. Line 1 costs $50 per hour to
operate and line 2 costs $55 per hour. Overtime is available for line 1 at $15 per hour
and for line 2 at $12 per hour. Management goals in decreasing order are:
P1: Produce 300 units.
P2: Maximum allowable overtime of 6 hours for line 1.
P3: Cost of overtime must not exceed $750.
P4: Avoid the underutilization of either production line. Assign weights that are
proportional to their production capability.
P5: Producing more than 300 units is 1-1/2 times as undesirable as producing under 300
units.
What is the objective function?
Minimize P1Ad1
The XYZ manufacturing company produces ball bearings. The annual fixed cost is
$20,000 and the variable cost per ball bearing is $3. The price is related to demand
according to the following equation: 1000 - 8p.
Determine the quantity of soap and shampoo that should be produced to maximize
profit.
Consider the following linear program, which maximizes profit for two
products--regular (R) and super (S):
MAX 50R + 75S
s.t.
1.2 R + 1.6 S ≤ 600 assembly (hours)
0.8 R + 0.5 S ≤ 300 paint (hours)
.16 R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
If downtime reduced the available capacity for painting by 40 hours (from 300 to 260
hours), profits would be reduced by ________.
A group of friends are planning a recreational outing and have constructed the
following payoff table to help them decide which activity to engage in. Assume that the
payoffs represent their level of enjoyment for each activity under the various weather
conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are
0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected
value criterion?
Given the following linear programming problem:
maximize 4x1 + 3x2
subject to 4x1 + 3x2 ≤23
5x1 - x2 ≤ 5
x1, x2 ≥ 0
What are the Cj values for the basic variables?
A manager has just received a revised price schedule from a vendor. What order
quantity should the manager use in order to minimize total costs? Annual demand is
120 units, ordering cost is $10, and annual carrying cost is $1 per unit.
In a factory, machines breakdown at an average of 6 machines per hour according to a
Poisson distribution. The time a repair person takes to repair the machine is not defined
by any probability distribution, but has a mean of 8 minutes and a standard deviation of
3 minutes.On average, how many machines are waiting in line to be fixed?
