Expected opportunity loss is the expected value of the regret for each decision.
There is exactly one optimal solution point to a linear program.
Constraints for nonlinear programs are usually nonlinear.
The mathematical steps in the simplex method replicate the process in graphical
analysis of moving from one extreme point on the solution boundary to another.
In a mixed integer model, some solution values for decision variables are integer and
others can be non-integer.
A marginal probability is the probability of a single event occurring.
When the right-hand sides of two constraints are both increased by one unit, the value
of the objective function will be adjusted by the sum of the constraints’ prices.
The term continuous is synonymous with divisible in the context of linear
programming.
For a typical normally distributed random variable, the standard deviation is equal to
the variance.
Multiple optimal solutions occur when constraints are parallel to each other.
A prohibited route in a transportation model should be assigned a value of zero.
Regression methods attempt to develop a mathematical relationship between the item
being forecast and factors that cause it to behave the way it does.
The objective function in a goal programming model seeks to minimize the deviation
from goals in the order of the goal priorities.
A minimization model of a linear program contains only surplus variables.
Goal constraints can include all deviational variables.
The objective function is a linear relationship reflecting the objective of an operation.
As the level of service improves, the cost of service decreases.
In systems with finite queue length, the service rate does not have to exceed the arrival
rate.
Inventory costs include carrying, ordering, and shortage costs.
A transition matrix cannot cause the system to cycle between states.
Graphical solutions to linear programming problems have an infinite number of
possible objective function lines.
Server utilization in a multiple-server system is calculated the same as in a single-server
system.
The simplex method can be used to solve quadratic programming problems.
Periodic inventory systems normally require smaller safety stock than a continuous
inventory system.
The expected value of perfect information divided by the expected value of sample
information is the efficiency of perfect information.
Parameters are known, constant values that are usually coefficients of variables in
equations.
The supply and demand values along the outside rim of a tableau are called rim
requirements.
The terms in the objective function or constraints are additive.
Linear programming models exhibit linearity among all constraint relationships and the
objective function.
The last step of the minimal spanning tree solution method is to make sure all nodes
have joined the spanning tree.
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.Which of the following is not a feasible production combination?
A) 0L and 0V
B) 0L and 1000V
C) 1000L and 0V
D) 0L and 1200V
The Lagrange multiplier is ________ to the dual variables in a linear programming
problem.
A) analogous
B) contradictory
C) inversely related
D) opposite
Sometimes manual simulation of several trials is ________ way to validate a
simulation.
A) a good
B) a bad
C) no
D) the only
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 optimal stock out level?
A) 96.44
B) 102.36
C) 108.44
D) 114.64
The following table represents the cost to ship from Distribution Center 1, 2, or 3 to
Customer A, B, or C.
The constraint that represents the quantity supplied by DC 1 is:
A) 4X1A + 6X1B + 8X1C ≤ 500.
B) 4X1A + 6X1B + 8X1C = 500.
C) X1A + X1B + X1C ≤ 500.
D) X1A + X1B + X1C = 500.
Solve the following integer linear program:
MAX Z = 2 +
subject to: 2 + 2 ≤ 7
4 + ≤ 11
and ≥ 0
What are the optimal values of x1 and x2?
A) x1 = 1, x2 = 3
B) x1 = 4, x2 = 1
C) x1 = 0, x2 = 3
D) x1 = 3, x2 = 2
E) x1 = 2, x2 = 2
Elements of project planning include:
A) identifying time-cost tradeoffs.
B) determining the project critical path.
C) comparing project schedule objectives.
D) all of the above
For a maximization linear programming problem, a(n) ________ is ________ for a
less-than-or-equal-to constraint.
A) surplus, subtracted
B) slack, added
C) artificial, added
D) artificial, subtracted
E) surplus, added
A professor’s son, having made the wise decision to drop out of college, has been
finding his way in life taking one job or another, leaving when his creativity is overly
stifled or the employer tires of his creativity. The professor dutifully logs the duration of
his son’s last few careers and has determined that the average duration is normally
distributed with a mean of eighty-eight weeks and a standard deviation of twenty
weeks. The next career begins on Monday; what is the likelihood that it endures for
more than two years?
A) 25%
B) 21%
C) 15%
D) 11%
The maximin criterion results in the:
A) minimum of the maximum payoffs.
B) maximum of the maximum payoffs.
C) maximum of the minimum payoffs.
D) minimum of the minimum payoffs.
A dummy activity is used to show a precedence relationship, but it does not represent a:
A) relationship between activities.
B) change in relationship.
C) real activity.
D) passage of time.
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.
Tim is wary of large crowds and won’t approach the soda machine if there are five or
more people at the machine. What percentage of the time does Tim forego a soda due to
the large crowd?
A) 30%
B) 20%
C) 13%
D) 9%
Which of the following statements about infeasible problems is best?
A) All of the possible solutions violate at least one constraint.
B) All of the possible solutions violate all of the constraints.
C) At least one of the possible solutions violates all of the constraints.
D) At least one of the possible solutions violates at least one of the constraints.
A linear programming model of a media selection problem is used to determine the
relative value of each advertising media.
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 MAD.
What is the mean absolute deviation for this forecasting approach?
A) 53.3
B) 57.9
C) 63.6
D) 67.3
Which of the following statements is not true?
A) An infeasible solution violates all constraints.
B) A feasible solution point does not have to lie on the boundary of the feasible
solution.
C) A feasible solution satisfies all constraints.
D) An optimal solution satisfies all constraints.
Game theory assumes that players behave:
A) logically.
B) emotionally.
C) rationally.
D) A, B, and C
E) A and B
The following is a graph of a linear programming problem. The feasible solution space
is shaded, and the optimal solution is at the point labeled Z*.
Which of the following
constraints has a surplus greater than 0?
A) BF
B) CG
C) DH
D) AJ
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.
What are the optimal daily production quantities of each product and the optimal daily
profit?
A) R = 75, D = 90, Z = $405
B) R = 135, D = 0, Z = $405
C) R = 90, D = 75, Z = $420
D) R = 40, D= 100, Z = $320
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:
If the forecast for period 5 is equal to 275, use exponential smoothing to compute a
forecast for period 7 if α = .40.
A) 273
B) 277
C) 267.8
D) 286.2
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 an appropriate constraint for this scenario?
A) ZG + YG + XG + WG + VG ≤ 1
B) ZG + YG + XG + WG + VG = 1
C) 9ZG + 3YG + 4XG + 1WG + 4VG ≥ 1
D) 9ZG + 3YG + 4XG + 1WG + 4VG = 1
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 their economic order quantity?
A) 40.6 cases
B) 162.5 cases
C) 406 cases
D) 1649.9 cases
The Taco Barn
After tallying the receipts for their first year of operation, the owners of the Taco Barn
are encouraged. Sales of their artisnal tacos, made from such exotic ingredients as
ground beef, cheese, and beans, have been strong and seem to give hope to the coming
year. Taco sales by month are shown in the table.
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. His fingers are aching by the time he reaches March
and he is worried about his ability to stuff tacos during tomorrow’s dinner rush. Help him
out by finding the forecast for April.
A) 583.5
B) 482.8
C) 497.4
D) 588.0
For the following transition matrices, what is the absorbing state(s)?
A) state 1
B) state 2
C) state 3
D) state 4
E) state 2 and 4
The basic feasible solution in the initial simplex tableau is the origin where all decision
variables equal:
A) o
B) 1
C) -1
D) 1 or -1
William ran the model in Excel and received both an answer and sensitivity report.
Which of these statements about this portion of the sensitivity report is best?
A) William needs 73 hours to produce.
B) William needs 2.5 additional bushels of corn.
C) William has 7.5 pounds of sugar more than he needs.
D) William needs 1 more hour to produce.
The manager of the Quick Stop Corner convenience store (which is open 360 days per
year) sells four cases of Stein soda each day (1440 cases per year). Order costs are
$8.00 per order. The lead time for an order is three days. Annual holding costs are equal
to $57.60 per case.If the daily demand is 50 and the lead time in days is 4, what is the
reorder point?
A) 200
B) 220
C) 240
D) 260
In the simplex procedure, if cj– zj = 0 for a non-basic variable, this indicates that:
A) the solution is infeasible.
B) the solution is unbounded.
C) there are multiple optimal solutions.
D) the formulation is incorrect.
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.)
What is an appropriate objective function for this scenario?
A) Max Z = 5,000N + 3,000R + 700T + 200F
B) Max Z = 500N + 250R + 125T + 15F
C) Min Z = 500N + 250R + 125T + 15F
D) Min Z = 5,000N + 3,000R + 700T + 200F
________ are the values that express the state of the system being modeled at the
beginning of the Monte Carlo simulation.
A) Outputs
B) Random events
C) Initial conditions
D) Random numbers
The efficiency of sample information is the ratio of the expected value of sample
information to the:
A) expected value of perfect information.
B) expected value.
C) utilization rate.
D) coefficient of optimism.
The linear programming model for a transportation problem has constraints for:
A) supply at each source.
B) supply at each source and demand at each destination.
C) demand at each destination.
D) a feasible solution.
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 a three-period moving average forecast for the month of July?
A) 47.33
B) 46.10
C) 45.38
D) 44.29
Armed only with his fingers, the owner decides that the safest forecasting approach is a
linear trend line. 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) 33.3
B) 21.7
C) 28.2
D) 25.9
The optimal integer solution will always be between the ________ bound of the relaxed
solution and a lower bound of the rounded-down integer solution.
A) lower
B) optimal
C) upper
D) all of the above
The basic EOQ model assumes that ________ is known with certainty and is relatively
constant over time.
Spring is right around the corner and that can mean only one thing: it’s time to incubate
some eggs for a fresh crop of chickens to supplement the existing flock for the year.
There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and
each has its own strengths and weaknesses. The Leghorns, for example, are superb
layers but easily excitable. The Cochins, on the other hand, are very even-tempered but
not the best layers. They do have marvelous plumage, with feathers that extend down to
their feet. The Buff Orpingtons are good layers, have interesting plumage, and are
mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as
possible while keeping the noise to a dull roar and having a nice array of birds
free-ranging on his lawn during those lazy summer days. He has put the relevant data in
table form. Plumage numbers are on a scale from 1-10, with 10 being the most
desirable. The egg output is not on a scale, but is instead the average output for the
breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and
crowing and is measured in decibels per bird. Appetite is measured in ounces of layer
pellets per week consumed by each of the breeds, while fertilizer is measured as the
output in ounces per week.
How should the objective function read?
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.
What is the formulation for this problem?
The first day on the cruise was a “day at sea” meaning no port of call, and only the
amenities onboard for amusement. Restless and uncomfortably full after seven trips
through the buffet, the management scientist gambled away most of his vacation money
at the onboard casino. The excursions would be a necessity, but now it became less
important to maximize the joy of the excursions and more vital to get off the boat as
cheaply as possible while still staying busy at the three ports of call. What is an
appropriate model for this modified cruise vacation?
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.
How many constraints does this model have? Provide a description in English for each
one, without writing it mathematically.
A graphical representation of a linear program is shown below. The shaded area
represents the feasible region, and the dashed line in the middle is the slope of the
objective function.
If this is a maximization, which extreme point is the optimal solution?
A multiple channel queuing system with a Poisson arrival rate and exponential service
time has an average arrival rate of 6 customers per hour and an average service time of
20 minutes per customer. What is the minimum number of servers required to avoid an
overloaded system?
Comedy Pasture
A horse and two llamas are discussing the key areas of their domain on a lazy summer
afternoon. The llamas favor the pond and shade and like to browse the fruit trees and
oaks on the property, making their way to the barn only when their owner favors them
with some oats. The horse prefers to graze the grass and hay for food and drink from the
pond but will race up to the barn when the owner is handing out oats up there. Between
the three of them, they have stepped off the distances between many of these key points
several times and believe that they have developed an accurate map, shown below. As
incredible as it may seem, neither the horse nor the llamas have had any training in
management science, which is where you come in.
The horse isn’t crazy about it, but occasionally will relent and pull a cart laden with
supplies from the barn to the other points of mutual interest, the grassy area, the pond,
and the hay down in the run in shed. What is the shortest distance from the barn to each
of these points?
Consider the following linear program:
MAX Z = 60A + 50B
s.t. 10A + 20B ≤ 200
8A + 5B ≤ 80
A ≥ 2
B ≥ 5
Solve this linear program graphically and determine the optimal quantities of A, B, and
the value of Z.
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.
Write the objective function for this problem.
Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to
warehouses and retail outlets. The network diagram given in the figure below shows the
possible routes and travel times (in minutes) from the carpet plant to the various
warehouses or retail outlets.
V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M =
Merillville, L = Lansing
Draw the network associated with the following constraints for a shortest route
problem.
X12 + X13 = 1
X12 – X24 = 0
X13 – X34 = 0
X24 + X34 – X45 = 0
X45 = 1
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 3-day moving average.
If he uses the minimax regret criterion, how many new workers will he hire?
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 group chooses to minimize their maximum regret, what activity will they choose?
Given the nonlinear programming model Max Z = 5x1 – 2x2
2
Subject to: x1 + x2 = 6
What is the optimal value of the Lagrange multiplier?