The ________ problem deals with the distribution of goods from several sources to
several destinations.
A) network
B) assignment
C) transportation
D) transshipment
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.What is the probability
that there are no customers in the grocery store?
A) .166
B) .333
C) .5
D) .667
The Lagrange multiplier is ________ the dual variables in a linear programming
problem.
A) analogous to
B) contradictory to
C) inversely related to
D) the opposite of
The Salt Creek Soap Company has determined the following nonlinear model to
determine the optimal pounds of industrial soap (X1) and shampoo (X2) it should
produce each day.
Maximize Z = X1
2 + 2X2
2 – 8X1– 12X2 + 34
Subject to: X1 + 2X2 = 4 lbs
What quantities of soap and shampoo maximize profit?
A) X1 = 0, X2 = 2
B) X1 = 1, X2 = 2
C) X1 = 2, X2 = 2
D) X1 = 2, X2 = 1
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.
How many units of Product A can they expect to sell?
A) 20,000
B) 17,000
C) 16,000
D) 15,000
The LS and LF are calculated using the:
A) backward pass through the network.
B) forward pass through the network.
C) values for ES and EF.
D) backward and forward pass through the network.
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:
Use a 3-period moving average to forecast demand for period 7.
A) 283.33
B) 280
C) 290
D) 310
It’s time to buy pet food again and Lisa heads to the grocery store with $40 in her purse,
leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can
and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat
only one can. Lisa would like to buy enough food to last through her three-day
weekend. What is an appropriate objective function for this scenario?
A) Min Z = 1D + 0.5C
B) Min Z = 2D + 1C
C) Min Z = D + C ≤ 40
D) Min Z = D + C ≥ 3
The ________ is the probability of moving from one state to another during one time
period.
A) transition probability
B) state of the system
C) steady-state probabilities
D) transition matrix
The purpose of inventory management is to determine:
A) timing and cost of orders.
B) quantity and cost of orders.
C) timing and quantity of orders.
D) ordering and carrying costs.
Semester Prep
The department chair reviewed last year’s schedule, the degree requirements for the
ever popular Operations and Supply Chain major, and the emails that had drifted into
her mailbox over the last week. Naturally, every professor in the department had his
own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all
costs. In an effort to placate the senior faculty members of the department, the chair
sent an email asking them to supply the prep time for each of the classes they were
qualified to teach, promising to assign them the least taxing schedule possible. Each of
her department members had to teach at least two courses, but no more than three. The
elective courses, Project Management, Quality Management, Control and Planning,
Logistics, and Management Science each had to be offered once and the department
needed to offer at least six sections of the Introduction to Operations class. The prep
times each professor estimated for each course appear in the table below.
David is qualified to teach Management Science, but has misplaced his slide rule and
doesn’t feel he can complete the necessary calculations if he is assigned to teach it next
semester. Which of these constraints would ensure that he isn’t the instructor?
A) DI + DP + DQ + DC + DL ≥ 2
B) SM + GM + TM + DM ≤ 1
C) DM = 0
D) DI + DP + DQ + DC + DL + DM ≤ 3
Which of the following are assumptions or requirements of the transportation problem?
A) Minimum quantities must be shipped.
B) Shipping costs per unit do not vary with the quantity shipped.
C) There can only be one source.
D) all of the above
The landlord uses the following scheme for decision variables:
Which of these constraints would not be appropriate for this scenario?
A) 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8≤ 3000
B) 1x1 + 2x2 + 1.5x3 + 3x4 + 5x5 + 1x6 + 0.25x7 + 0.5x8≤ 4
C) x3 + x4 = 1
D) x1, x2, x3, x4, x5, x6 , x7, x8≥0 and integer
A store has determined that the weekly sales of a product is related to the number of
customers who visit the store and the square feet of shelf space, x, according to the
following equation: -20x2 – 10C2 + 40Cx + 120x – 200. C represents the hundreds of
customers who visit their store. If a store averages 200 customers per week, how many
square feet of shelf space is required to maximize sales?
A) 3
B) 4
C) 5
D) 1 or 9
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.
The stockbroker suggests limiting the investments so that no more than $10,000 is
invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350,
whichever is more restrictive. How would this be formulated as a linear programming
constraint?
A) X2 ≤ 10000
X2 + X3 ≤ 350
B) 10,000 X2 ≤ 350X2 + 350X3
C) 25X2 ≤ 10,000
X2 + X3 ≤ 350
D) 25X2 ≤ 10,000
25 X2 + 110X3 ≤ 350
________ is the Difference between the forecast and actual demand.
A) Forecast mistake
B) Forecast error
C) MAD
D) Forecast accuracy
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 objective function is:
A) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 + 25X35 + 6X36 + 17X37 + 29X45
+ 8X46 + 5X47.
B) MIN 7X13 + 8X14 + 4X23 + 7X24 – 3X34 – 3X43 + 25X35 + 6X36 + 17X37 + 29X45 +
8X46 + 5X47.
C) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 – 25X35 – 6X36 – 17X37 – 29X45 –
8X46 – 5X47.
D) MIN 7X13 + 8X14 + 4X23 + 7X24 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47.
The result of an effective decision making process should be monitored in order to:
A) reveal the break-even point.
B) reveal errors in the implementation.
C) keep fixed and variable costs distinct.
D) change the scientific method.
Developing the cumulative probability distribution helps to determine:
A) simulation numbers.
B) data sets.
C) random number ranges.
D) mean of the distribution.
Assume that a decision maker has to make a choice between three types of cars. Chevy,
Honda, and Ford. Based on three criteria: comfort, MPG, and style.
The row averages for criteria is summarized in the following column vector:
The first row of the following matrix represents Chevy, the second row represents
Honda, and the third row represents Ford.
The preference matrix for the three types of cars is given as follows:
Compute the overall score for each decision alternative (car). Which choice does the
decision maker prefer?
A) Chevy
B) Honda
C) Ford
D) Honda and Chevy are equally preferred.
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.
Which of these changes would have no effect on which supplier is chosen in the output
range of 0 units to 20,000 units?
A) Variable costs fall 10% for all bidders.
B) Fixed costs rise 10% for all bidders.
C) Companies A and B swap their figures for fixed costs.
D) Companies C and D swap their figures for fixed costs.
A business professor wishes to model the duration of his commute through the busy
streets of Bangalore. He decides to model it based on the number of auto-rickshaws that
he passes during the first ten minutes of the drive. The continuous probability
distribution 7x – 2 serves as a good model.
What is the integral from 5 to 7 for this distribution?
A) 14
B) 36
C) 80
D) 66
Consider the following frequency of demand and random numbers:
Random numbers: 0.13, 0.81, 0.53.
If the simulation begins with the first random number, the simulated value for demand
would be:
A) 0
B) 1
C) 2
D) 3
Objective probabilities that can be stated prior to the occurrence of an event are:
A) deterministic or probabilistic.
B) subjective or objective.
C) classical or a priori.
D) relative or subjective.
An important factor to consider in analyzing a queuing system is the:
A) queue discipline.
B) queue structure.
C) queue order.
D) cost.
A business professor wishes to model the duration of his commute through the busy
streets of Bangalore. He decides to model it based on the number of auto-rickshaws that
he passes during the first ten minutes of the drive. The continuous probability
distribution 7x – 2 serves as a good model.
What is the integral from 0 to 5 for this distribution?
A) 33
B) 77.5
C) 59
D) 63
Pickmeup is a drive through coffee house that has room for 3 cars in the driveway. The
line cannot exceed 3 cars, and because they are exclusively drive through, customers
may be turned away. In the morning, the arrival rate is 40 cars per hour (Poisson
distributed) and with the servers working in teams, they can process 50 cars per hour
(the service rate is exponential). What is the probability of turning customers away?
A) .173
B) .210
C) .339
D) .410
The upper bound at the initial node of a branch and bound tree is given by
A) the value of the objective function of the LP relaxation .
B) the value of the objective function after the LP relaxation solution is rounded down
to an integer solution.
C) the value of the objective function corresponding to an integer feasible solution
determined on the basis of trial and error.
D) cannot be determined
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 the demand constraint.
A) 5x1 = x2
B) x1 – 2.5x2 ≥ 0
C) x1 + 2.5x2 ≤ 0
D) x1 = 2.5x2
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.
Mondo ran the problem in Excel but used “≤ 1” constraints everywhere instead of “= 1”
constraints. The objective function is formulated correctly and the general structure of the
constraints is also correct, except for the inequality.
What is a reasonable conclusion that can be drawn from this formulation of the model?
A) None of the outfits will be worn.
B) There would be no difference in the model results from one with = constraints.
C) A model may be assigned two different outfits.
D) An outfit may be assigned to two different models.
In a ________ distribution, for each of n trials, the event always has the same
probability of occurring.
A) binomial
B) joint
C) frequency
D) standard
After calculating the EOQ and informing their supplier of their order amount, they are
informed that the supplier is reluctant to break a case, that is, there are 10,000 swizzle
sticks in a case and they must be ordered in multiples of that amount. Not wanting to
understock, the krewe decides to round up to the next highest multiple of 10,000. What
is the decrease in ordering cost if they order at this amount?
A) $36.75
B) $32.50
C) $41.93
D) $33.96
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 B will being purchased by the smaller company?
A) 0.8
B) 0.5
C) 0.4
D) 0.3
The objective function coefficient of an artificial variable for a minimization linear
programming problem is:
A) +M.
B) -M.
C) 0
D) 1
E) an arbitrary value between 0 and positive infinity
Two or more goals at the same priority level can be assigned weights to indicate their
relative:
A) meaning.
B) slack.
C) difference.
D) importance.
A ________ probability is the probability that an event will occur given that another
event has already occurred.
A business is trying to decide which restaurant to hold its annual awards banquet. Use
the information below to determine the best choice.
Restaurant
A(n) ________ occurs when the optimal strategy for each player results in the same
payoff.
Solve the following graphically:
Max z = 3x1 + 4x2
s.t. x1 + 2x2 ≤ 16
2x1 + 3x2 ≤ 18
x1 ≥ 2
x2 ≤ 10
x1, x2 ≥ 0
What are the optimal values of x1, x2, and z?
A ________ game occurs when each player selects an optimal strategy that does not
result in an equilibrium point when the minimax criterion is used.
A company markets educational software products, and is ready to place three new
products on the market. Past experience has shown that for this particular software, the
chance of ‘success” is 80%. Assume that the probability of success is independent for
each product.
Find the probability that exactly 1 of the 3 products is successful.
Formulate all elements of linear program to model your university effort. Include a
narrative that explains each of the components.
Given the following data on hotel check-ins for a 6-month period:
July: 70 rooms
August: 105 rooms
September: 90 rooms
October: 120 rooms
November: 110 rooms
December: 115 rooms
If the forecast is 25 and the actual value is 25, then the error this period is ________.
A ________ is a functional relationship including variables, parameters, and equations.
Corner points on the boundary of the feasible solution area are called ________ points.
A ________ represents a limitation to achieving maximum profits due to limited
resources.
Canning Transport wants to move goods from three (3) factories to three (3) distribution
centers. Information about the move is given below:
Shipping costs are (in $):
According to the minimum cell cost method, the initial solution would have a total
transportation cost of ________.
Lenny, a graduate research assistant “moonlights” at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
Instead of having another student help Lenny, the manager is thinking of having two
lines instead. Customers will equally divide themselves between the two lines. How
long will students wait in line if there’s a second server? (Assume that the service time
is 5 minutes.)
Lenny, a graduate research assistant “moonlights” at the short order counter in the
student union snack bar in the evenings. He is the only one on duty at the counter
during the hours he works. Arrivals to the counter seem to follow the Poisson
distribution with a mean of 8 per hour. Each customer is served one at a time and the
service time follows an exponential distribution with a mean of 5 minutes.
How long will a student wait in line, on average?
The reorder point will ________ if lead time increases and demand per day remains the
same.
In a bank drive-through, there is a single service window and room only for two cars to
line-up to wait for service. The mean time between arrivals for drive through customers
is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The
number of arrivals is distributed according to a Poisson distribution and the service
times are exponentially distributed.
On average, how many cars are in the system?