A single-server queuing system has average time between arrivals of 20 minutes and a
service time of 10 minutes each. Assuming Poisson arrivals and exponential service
times, the utilization factor is approximately:
A) 0.25.
B) 0.33.
C) 0.50.
D) 2.0.
The production manager for the Coory soft drink company is considering the
production of two kinds of soft drinks: regular and diet. 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.
For the production combination of 135 cases of regular and 0 cases of diet soft drink,
which resources will not be completely used?
A) only time
B) only syrup
C) time and syrup
D) neither time nor syrup
Both linear and nonlinear programming models are examples of:
A) goal programming models.
B) simplex tableaus.
C) constrained likelihood models.
D) constrained optimization models.
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 6, what
is the standard deviation of the average length of the next five contracts?
A) 1.414
B) 1.250
C) 1.166
D) 1.083
When the poultry farmer runs his linear programming model, he discovers that his flock
will consist entirely of Leghorn birds. He studies his sensitivity report (copied below)
and decides to write a constraint that requires two Cochin chickens to be selected. If the
current optimal mix of breeds results in 160 eggs per week, which of the following
statements is best?
A) The new weekly egg output will be 169.
B) The new weekly egg output will be 162.
C) The new weekly egg output will be 158.
D) The new weekly egg output will be 153.
The ________ form of a linear program is used to determine how much one should pay
for additional resources.
A) standard
B) primal
C) feasible
D) dual
E) simplex
In order to attract listeners, a radio station gives away money if listeners correctly
identify the amount of money found by a “treasure hunter”. A contestant would guess
the amount on the air, and the disc jockey would then play a tape in which the “treasure
hunter” said how much he had found. If the caller guessed correctly, they won the
amount of money found by the treasure hunter. If they guessed incorrectly, they
received nothing. Suppose that the treasure hunter either found $50 or $100. The payoff
matrix represents this game:
If the station plans on running the game every day for 10 days, how much will they pay
out?
A) $250
B) $333
C) $500
D) $750
E) $667
________ is the percentage of the variation in the dependent variable that results from
the independent variable.
A) Regression
B) Coefficient of determination
C) Correlation
D) Linear regression
At the initial basic feasible solution at the origin, only ________ variables have a value
greater than zero.
A) linear
B) slack
C) non-linear
D) integer
Armed only with his fingers, the owner decides that the safest forecasting approach is
exponential smoothing with an alpha of 0.8. He uses the January demand and the
January forecast just to get the ball rolling. Generate a forecast for the year using this
technique and then calculate forecast errors using MAD. What is the mean absolute
deviation for this forecasting approach?
A) 41.3
B) 45.8
C) 49.9
D) 58.8
A decision with more than one objective:
A) should be decomposed into a separate model for each objective.
B) depends on the probability of satisfying each objective.
C) requires the decision maker to put the objectives in some order of importance.
D) cannot have an optimal solution.
Classification of management science techniques does notrecognize:
A) linear mathematical programming.
B) probabilistic techniques.
C) network techniques.
D) computer programming.
A ________ deviational variable is the amount by which a goal level is exceeded.
A) negative
B) positive
C) positive or negative
D) positive and negative
Poultry Processing processes chickens for fast food restaurants. The chickens arrive
from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the
Poisson distribution. The quality standards of Poultry Processing require that the
chickens be processed within 30 minutes, which includes the time from when the trucks
arrive until the chickens are finished processing. What is the minimum average
processing rate (in truckloads per hour) that must be designed for the machine in order
to ensure that the cages will be processed, on the average, in 30 minutes or less?
Assume processing time is exponentially distributed.
A) 5 trucks per hour
B) 9 trucks per hour
C) 10 trucks per hour
D) 18 trucks per hour
The production manager for the Coory soft drink company is considering the
production of two kinds of soft drinks: regular and diet. 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.
Which of the following is not a feasible production combination?
A) 90R and 75D
B) 135R and 0D
C) 75R and 90D
D) 40R and 100D
If the feasible region for a linear programming problem is unbounded, then the solution
to the corresponding linear programming problem is ________ unbounded.
A) always
B) sometimes
C) never
D) There is not enough information to complete this statement.
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 C and alternative D.” What coefficient of optimism would
make the cold, calculating father indifferent between these two alternatives?
A) 0.096
B) 0.125
C) 0.167
D) 0.183
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.
The basic decision environment categories are:
A) certainty and risk.
B) risk and uncertainty.
C) certainty and uncertainty.
D) certainty, uncertainty and risk.
Administrators at a university will charge students $150 to attend a seminar. It costs
$3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs
$25 per student for the administrators to provide the course materials. How many
students would have to register for the seminar for the university to break even?
A) 18
B) 20
C) 24
D) 30
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.
Which of the following constraints represents the assignment for task 2, scanning?
A) X2A + X2B + X2C = 0
B) X2A + X2B + X2C = 1
C) X2A + X2B + X2C ≤ 1
D) X2A + X2B + X2C ≥ 0
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 will be their
annual holding cost if they produce the optimal batch size?
A) 58.63
B) 62.20
C) 65.77
D) 69.34
A linear programming model solution with no integer restrictions is called a(n)
________ solution.
A) optimal
B) feasible
C) relaxed
D) all of the above
The local grocery store consists of two cashiers. The customers arrive at the checkout
according to the Poisson distribution and the service times are based on negative
exponential distribution. The average customer service time is 4 minutes and the
average time between the arrivals of successive customers is 3 minutes. Assume that
customers equally divide themselves between the two cashiers.How much time is a
customer expected to spend waiting in line and checking out?
A) 8 minutes
B) 12 minutes
C) 16 minutes
D) 20 minutes
Mutually exclusive events are:
A) events with identical probabilities.
B) events that have no outcomes in common.
C) events that have no effect on each other.
D) events that are represented in a Venn diagram by two overlapping circles.
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 transshipment through the distribution center?
A) 2X13 + 3X23 = 900
B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0
C) X13 + X23 – X34 – X35 – X36 = 0
D) X13 + X23 – X34 – X35 – X36 ≥ 0
Jolt – Exp
The soda machine outside the lecture hall sees a steady stream of customers throughout
the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water
once the button is pressed, the student customers introduce variation into the delivery
process by pondering their selection for a while. Thus, we can safely say that the
service time is governed by a negative exponential probability distribution that averages
10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of
240 per hour, Poisson distributed of course.
Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the
classroom and ignore any requests to enter the room once his scintillating lecture has
begun. Nathan approaches the soda machine at 9:59:20. Will he make it to class on
time?
A) Nathan will be late by ten seconds.
B) Nathan will be exactly on time.
C) Nathan will be early by ten seconds.
D) Nathan will be early by twenty seconds.
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.
The constraint for the quantity shipped from Madison is:
A) X13 + X 14 = 1000.
B) X13 + X 14 ≤ 1000.
C) X13 + X 14 ≥ 1000.
D) X13 + X 14 – X34 = 1000.
Sara’s Sensible Critters makes two kinds of catnip toys: balls (x1) and mice (x2). The
relationship between demand and price for balls and mice is:
x1 = 1800 – 150p1
x2 = 1500 – 300p2
The cost for a catnip ball is $2 and for the mouse, $3.
Sara has only 200 ounces of catnip on hand. A ball uses a tenth of an ounce and a toy
mouse uses one-quarter of an ounce.
Write the appropriate expression for profit.
A) Max Z = (p1 – 3)x1 + (p2 – 2)x2
B) Max Z = (p1 + 2)x1 + (p2 + 3)x2
C) Max Z = (p1 – 2)x1 + (p2 – 3)x2
D) Min Z = (p1 – 2)x1 + (p2 – 3)x2
Compared to blending and product mix problems, transportation problems are unique
because:
A) they maximize profit.
B) the constraints are all equality constraints with no “≤” or “≥” constraints.
C) they contain fewer variables.
D) the solution values are always integers.
Elements of project planning include:
A) defining project objectives.
B) identifying activities to crash.
C) calculating expected times and standard deviations.
D) conducting a “lessons learned” session.
Under the normal curve, the area between z = 1 and z = -2 includes approximately
________ of the values.
A) 98%
B) 95%
C) 85%
D) 82%
A tabular presentation that shows the outcome for each decision alternative under the
various possible states of nature is called a:
A) decision tree.
B) payoff table.
C) feasible region.
D) payback matrix.
The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and
because he found their gentle clucking to relax him as he worked on his laptop on his
deck. Their movements around his yard gave meaning to the term random walk you
literally could not predict their location from one minute to the next. His collection of
birds is neatly summarized in this table.
A Rhode Island Red just joined him up on the deck; what is the probability it is a
rooster?
A) 0.20
B) 0.30
C) 0.33
D) 0.37
A manager is trying to improve a single-server queueing system through automation.
The average service time is 20 minutes per customer, exponentially distributed, and the
arrival rate is 16 customers per 8-hour day (Poisson arrivals). The automated system
will have a constant service time of 16 minutes. The effect of this change will:
A) decrease utilization.
B) increase waiting time.
C) decrease waiting time.
D) have no effect since the service time is unchanged.
Project control involves:
A) crashing.
B) three time estimates.
C) a backward or forward pass.
D) earned value analysis.
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.
If the first four random numbers are 17, 33, 64, and 8, what is the average number of
weeks?
You have been asked to select at least 3 out of 7 possible sites for oil exploration.
Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction Evaluating sites S1and S3 will prevent you from exploring site S7.
Restriction Evaluating sites S2or S4 will prevent you from assessing site S5.
Restriction Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint for the third restriction.
The owner of a seafood market determined that the average weight for a crab is 1.6
pounds with a standard deviation of 0.4 pound. Assuming the weights of the crabs are
normally distributed, what is the probability that a randomly selected crab will weigh
more than 2.2 pounds?
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.
If each contract is worth $4000 but it costs $200 per week to work on a contract, what is
the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94?
The daily sales of a peanut butter at Power’s Grocery are normally distributed, with a
mean of 12 jars and a standard deviation of 4. The manager checks the inventories on
shelves and places an order every three days. Delivery lead time is two days.
In a noninstantaneous receipt model, daily demand is 55 units and daily production is
120 units, Co = $70 and Cc = $4 per unit/year. The production facility operates 300 days
per year. What is the maximum inventory level?
The ________ model is an extension of the transportation model in which intermediate
points are added between the sources and destinations.
Solve the following integer LP using branch and bound:
MAX Z = + 5
subject to: + 10 ≤ 20
≤ 2
, ≥ 0 and integer
Consider the following distribution and random numbers:
If a simulation begins with the first random number, what would the first simulation
value would be ________.
The owner of a seafood market determined that the average weight for a crab is 1.6
pounds with a standard deviation of 0.4 pound. Assuming the weights of crabs are
normally distributed, the probability that a randomly selected crab will weigh less than
1.2 pounds is ________.
Consider the following transportation problem:
How many demand-side constraints are there? Write the demand-side constraints.
The manager is open to suggestions for forecasting models and decides to try both an
exponential smoothing model with an alpha of 0.9 and a simple moving average of two
periods. He decides to use the actual value for January as the forecast for February just
to get the exponential smoothing forecasting party started. For the moving average
approach, he uses the actual for January as the forecast for February and the actual for
February as the forecast for March before beginning to apply the moving average
equation. Generate forecasts for the year using these technique and then calculate
forecast errors using MAD to determine which is the superior method in this scenario.
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. What is the shortest route
from the source node (node 1) to nodes 2, 3, and 4? Indicate the total distance for each
route.
The analytical hierarchy process was used to determine which car to purchase. Four
criteria were used: price, miles per gallon, comfort, and durability. Consider the
following normalized matrix and the preference vector for durability.
Multiplying the normalized matrix by the preference vector gives the following results:
Compute the consistency index.
Small motors for garden equipment are produced at four manufacturing facilities and
need to be shipped to three plants that produce Different garden items (lawn mowers,
rototillers, leaf blowers). The company wants to minimize the cost of transporting items
between the facilities, taking into account the demand at the three Different plants, and
the supply at each manufacturing site. The table below shows the cost to ship one unit
between each manufacturing facility and each plant, as well as the demand at each plant
and the supply at each manufacturing facility.
Write the formulation for this problem.
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 plan recipients would receive payments beyond age 75?