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A point of equilibrium is a value that is simultaneously the minimum of a row and the
maximum of a column.
A posterior probability is the likelihood that an event has occurred after the decision
maker has reached a decision.
A Markov assumption is that the probabilities change over time.
A Markov assumption is that the probabilities apply to all system participants.
Markov analysis is not an optimization technique.
A management science technique usually applies to a specific model type.
The Lagrange multiplier reflects a change in the objective function from a unit change
in the right-hand-side value of a constraint.
The basic feasible solution in the initial simplex tableau is the origin where all decision
variables equal zero.
Random numbers are typically generated on the computer using a numerical technique.
The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.
Sensitivity analysis can be used to determine the effect on the solution for changing
several parameters at once.
Applications of simulation models reflecting continuous distributions are more common
than those of models employing discrete distributions.
Assignment linear programs always result in integer solutions.
The following equation represents a resource constraint for a maximization problem: X
+ Y ≥ 20.
Markov analysis provides a recommended decision.
Adjusted exponential smoothing is an exponential smoothing forecast adjusted for
seasonality.
All single-server queuing models require the utilization factor to be less than 1.
The state of the system is where the system is at a point in time.
Queue discipline refers to the willingness of customers to wait in line for service.
If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a
mutually exclusive constraint.
Transportation problems can have solution values that are non-integer and must be
rounded.
Data envelopment analysis problems are usually maximization problems.
Simulation results will always equal analytical results if 30 trials of the simulation have
been conducted.
The earliest finish time for the final activity on a project network is also the total
completion of the project.
A negative deviational variable is the amount by which a goal level is exceeded.
The slope of a curve at any point is equal to the derivative of the curve's function.
Decision trees can be used to solve for steady state probabilities.
The equation 8xy = 32 satisfies the proportionality property of linear programming.
An experiment is an activity that results in one of several possible outcomes.
Multiple optimal solutions cannot be determined from the simplex method.
Consider the following integer programming problem. Solve it using the branch and
bound method. What are the optimal values of x1, x2, and Z?
Maximize Z = 2x1 + x2
Subject to: 2x1 + 2x2 ≤ 7
4x1 + x2 ≤ 11
x1 and x2 ≥ 0
A) x1 = 1, x2 = 2, Z = 4
B) x1 = 2, x2 = 1, Z = 5
C) x1 = 1, x2 = 1, Z = 3
D) x1 = 0, x2 = 3, Z = 3
E) x1 = 2, x2 = 2, Z = 6
The slope of a curve at any point is ________ the derivative of the curves function.
A) smaller than
B) larger than
C) equal to
D) none of the above
A Markov assumption is that the probabilities apply to ________ system participants.
A) none of the
B) the major
C) some
D) all
In the linear programming formulation of a transportation network:
A) there is one variable for each arc.
B) there is one constraint for each node.
C) the sum of variables corresponding to arcs out of an source node is constrained by
the supply at that node.
D) all of the above
What is the reorder point for Stein soda?
A) 4 cases
B) 8 cases
C) 12 cases
D) 16 cases
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.
Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed
cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the
two bidders?
A) 3,250
B) 3,500
C) 3,750
D) 4,000
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
probability that the system is idle is:
A) 0
B) .20.
C) .40.
D) .60.
The derivative of a function ________ the slope of the curve defined by that function.
A) is larger than
B) equals
C) is smaller than
D) is similar to
The Hurwicz criterion is a compromise between the minimax and minimin criteria.
A university is planning an online seminar. It costs $30 to live stream an instructor from
Elbonia. Assume it costs $25 per student for the administrators to provide the course
materials. If we know that 20 people will attend, what price should be charged per
person to break even?
A) $55
B) $15
C) $26.50
D) $75.75
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. How long does it take to
produce the optimal batch size?
A) 10 weeks
B) 9 weeks
C) 8 weeks
D) 7 weeks
If Xab = the production of product a in period b, then to indicate that the limit on
production of the company's 3 products in period 2 is 400, we write:
A) X32 ≤ 400.
B) X21 + X22 + X23 ≤ 400.
C) X12 + X22 + X32 ≤ 400.
D) X12 + X22 + X32 ≥ 400.
Riverside Industries makes two products and each product is processed in three
departments. The time requirements for each product in each department are given
below. The profit for each product is also provided as well as the available hours in
each department.
Product Department A Department B Department C Profit
1 3 4 2 1
2 2 1 2 2
Available Hours 600 400 400
Management wants to achieve three goals. The first two goals are equal in priority.
Priority 1: Produce at least 125 units of product 1.
Priority 1: Produce at least 80 units of product 2.
Priority 2: Achieve a profit of at least 300.
The goal programming constraint for the first goal is:
A) 3x1 + d1
- - d1
+ = 125.
B) 3x1 - d1
- + d1
+ = 125.
C) 1x1 + d1
- - d1
+ = 125.
D) 1x1 - d1
- + d1
+ = 125.
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.
Over the range of demand shown by this graph, which action would completely remove
one of the potential suppliers from consideration?
A) lowering A's fixed cost by 10%
B) raising B's variable cost by 10%
C) raising C's variable and fixed costs by 10%
D) lowering D's fixed cost by 25%
A small entrepreneurial company is trying to decide between developing two different
products that they believe they can sell to two potential companies, one large and one
small. If they develop Product A, they have a 50% chance of selling it to the large
company with annual purchases of about 20,000 units. If the large company won't
purchase it, then they think they have an 80% chance of placing it with a smaller
company, with sales of 15,000 units. On the other hand if they develop Product B, they
feel they have a 40% chance of selling it to the large company, resulting in annual sales
of about 17,000 units. If the large company doesn't buy it, they have a 50% chance of
selling it to the small company with sales of 20,000 units.
What is the probability that Product A will being purchased by the smaller company?
A) 0.8
B) 0.5
C) 0.4
D) 0.2
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.
How many constraints are required to model this as a linear program?
A) 8
B) 9
C) 10
D) 12
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 appropriate criterion is dependent on:
A) the risk personality of the decision maker.
B) the number of nodes in the decision tree.
C) the magnitude of the payoffs.
D) none of the above
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
The maximin strategy is:
A) Buy.
B) Rent.
C) Lease.
D) Brisk.
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 demanded by Customer B is:
A) 6X1B + 2X2B + 8X3B ≤ 350.
B) 6X1B + 2X2B + 8X3B = 350.
C) X1B + X2B + X3B ≤ 350.
D) X1B + X2B + X3B = 350.
The manager is open to suggestions for forecasting models. Plot the data and discuss
the efficacy of the moving average, weighted moving average, exponential smoothing,
and trend as the relate to this data.
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 hen just joined him up on the deck; what is the probability it is an Australorp?
A) 0.18
B) 0.20
C) 0.22
D) 0.24
A 95% confidence interval is (54.5, 57.5) based on a sample size of What is the sample
standard deviation?
A) 3.826
B) 19.132
C) 8.973
D) 11.646
In multiple-server models, ________ independent servers in parallel serve a single
waiting line.
A) 2 or more
B) 3 or more
C) 4 or more
D) 5 or more
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest
project and recorded them using different colors of sand on a pristine slab of white
marble. She used red for late start and late finish times and green for early start and
early finish times. Activity durations and their identifiers were written with black sand.
She finished her task and had an opportunity to admire her work only briefly before a
colleague came by and swept most of it away. Sadly, this was before Carrie could
record the numbers on a more permanent medium, so now she turns to you to help.
What is the late start time for activity H?
A) 21
B) 24
C) 17
D) 23
Zevon Enterprises
Zevon Enterprises provides services for clients worldwide and to protect all parties to
this course as well as Zevon, we shall refer to those services as X1, X2, and X3. Each of
these services has its own special mix of needs for the resources the company has at its
disposal. The X1 product requires three lawyers, seven guns, and $6,000; the X2
product requires two lawyers, five guns, and $4,000; and the X3 product requires four
lawyers, six guns, and $7,000. Zevon has access to 5,000 lawyers, 10,000 guns, and
$15,000,000. For ease of conversation, Zevon employees usually speak about dollars as
"per thousand" so one of them asking for $7 means that they really need $7,000.
Zevon's demand is variable depending on what they charge for it. For example, the X1
product's demand is 200 - 2.25p1. The demand for X2 is 300 - 3p2, and the demand for
X3 is 400 - 3.5p3. The per unit profit forX1 through X3 can be calculated by subtracting
the per unit cost from the sales price, so for X1, the profit is p1 - 25, for X2 the profit is
p2- 3, and for X3 the profit is p3- 3.5.
What is an appropriate objective function for this scenario?
A) Max Z = (p1- 2.25)X1 + (p2- 3)X2 + (p3- 3.5)X3
B) Max Z = (p1- 2.25)(200 - 2.25p1) + (p2- 3)(300 - 3.00p2) + (p3- 3.5)(400 - 3.50p3)
C) Max Z = 200X1 + 300X2 + 400X3
D) Max Z = 2.25(p1- X1) + 3(p2- X2) +3.5 (p3- X3)
What is the proper interpretation of the shadow price for Facebook?
A) Every additional dollar spent on Facebook advertising gains 20 customers as long as
the number of postings does not exceed 233.
B) Every additional dollar spent on Facebook advertising gains 20 customers as long as
the number of postings does not exceed 229.
C) If they spend $4, then can reach 20 customers.
D) If they spend less than $20, they can reach 229.333 customers.
If the number of unique assignments is ________ the number of rows or columns, a line
test must be used.
A) more than
B) less than
C) higher than
D) equal to
Dinnertime
A professor is planning an informal gathering for 100 or so of his closest friends. The
project breaks down as follows:
Which activity has a slack time that is different from all others?
A) hire quartet
B) hire valets
C) schedule butler
D) schedule cleaning crew
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest
project and recorded them using different colors of sand on a pristine slab of white
marble. She used red for late start and late finish times and green for early start and
early finish times. Activity durations and their identifiers were written with black sand.
She finished her task and had an opportunity to admire her work only briefly before a
colleague came by and swept most of it away. Sadly, this was before Carrie could
record the numbers on a more permanent medium, so now she turns to you to help.
What is the slack time for activity C?
A) 3
B) 2
C) 1
D) 0
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
Construct the payoff matrix for the game, "rock, paper, scissors" for 2 players, A and B.
Assume that "paper covers rock," "rock breaks scissors," and 'scissors cut paper." If
player A wins, assign +1. If player A loses, assign -1.
________ is the analysis of the effect of parameter changes on the optimal solution.
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.
What is the complete linear model for this scenario?
The three methods for identifying initial feasible solutions to transportation problems
are ________, ________, and ________.
The Excel LP model for this scenario shows the following sensitivity report for the
constraints. Comment on the salient features.
A pure strategy game can be solved according to the ________ criterion.
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.
How many order per year will they place?
________ measures the strength of the relationship between two variables.
A balanced transportation model should have ________ constraints.
In an assignment problem, all demand and supply values are equal to ________.
Solve the following nonlinear program:
Min x1
2 + 2x2
2 - 8 x1 - 12x2 + 34
subject to: x1
2 + 2x2
2 = 5
________ is the probability that the inventory available during the lead time will meet
demand.
When a maximization problem is ________, the objective function can increase
indefinitely without reaching a maximum value.
Consider the following integer programming problem. Solve it using the branch and
bound method. What are the optimal values of x1, x2 and Z?
Maximize Z = 2x1 + x2
Subject to: 2x1 + 2x2 ≤ 7
4x1 + x2 ≤ 11
x1 and x2 ≥ 0
Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a
period of one month and assigned them to five different categories as shown in the
table.
What is the likelihood that the commute will take 30 minutes or longer?
Mad Over Donuts
An entrepreneurial resident of the Oklahoma City metropolitan area is interested in
securing a new franchise for Mad Over Donuts. Ideally this franchise would be
centrally located so delivery could be economically handled and all citizens could enjoy
fresh, delicious donuts delivered to the doorstep. The main cities and anticipated
demand (in thousands per day) are shown in the table.
Zoey's Catnip Toys faces the following relationship between price and demand: v = 2000 -
200p. The fixed cost is $500 and variable cost is $1. What price should Zoey charge to
maximize profit?
An online sweepstakes has the following payoffs and probabilities. Each person is
limited to one entry.
The probability that someone wins any money is ________.
The ________ command is used in generating the random numbers with Excel.
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.
"Cletus, my boy," he said to his dog that was dozing peacefully before the fireplace, "I
don't like to look back on my decisions with any regret. In fact, in my golden years I make
most of my decisions so that when I do look back, I have as little regret as possible." What
is the regret table and optimal choice given this state of mind?
