In general, an increase in price increases the break-even point if all costs are held
constant.
In the regression equation y=a+bx, the slope of the equation is x.
If variable costs increase, but price and fixed costs are held constant, the break-even
point will decrease.
The sensitivity range for an objective function coefficient is the range of values over
which the current optimal solution point (product mix) will remain optimal.
The maximin criterion maximizes the minimum regret.
The early start for an activity on the critical path is always equal to the earliest finish of
the preceding activity.
Markov analysis can be used to determine the steady state probabilities associated with
machine breakdowns.
The variance of a random variable is computed by multiplying each possible value of
the variable by its probability and summing these products.
The shadow price for a positive decision variable is 0.
An optimal solution occurs when the number of independent unique assignments equals
the number of rows or columns.
If a Lagrange multiplier equals 3, a one-unit increase in the right-hand side of a
constraint, will result in an increase of 3 in the objective function.
A work breakdown structure breaks down a project into subcomponents, components,
activities, and tasks.
The expected value of a random variable is computed by multiplying the sum of each
possible value of the variable by the probability of that random variable.
The Monte Carlo process is analogous to gambling devices.
The first step in solving a linear programming model manually with the simplex method
is to convert the model into standard form.
The most important factors to consider in analyzing a queuing system are queuing
discipline, arrival and service rate, and the nature of the calling population.
The early finish for an activity on the critical path is equal to the latest finish of the
preceding activity.
The number of servers, c, in a multiple-server queuing system must be greater than the
average queue length.
A strategy is a plan of action followed by a player.
Carrying costs include storage cost, interest, and depreciation.
Objective function terms are not summed in goal programming because not all goals are
achievable.
Time series methods assume that what has occurred in the past will continue to occur in
the future.
Markov analysis is not a probabilistic technique.
Classical optimization uses calculus to determine the optimal values of a variable.
The linear programming model for a transportation problem has constraints for supply
at each source and demand at each destination.
The sensitivity range for an objective function coefficient is the range of values over
which the profit does not change.
In a transshipment problem, items may be transported from destination to destination
and from source to source.
Technological forecasting helps determine the technological feasibility of new products
by surveying large numbers of consumers.
In a balanced transportation model where supply equals demand, all constraints are
equalities.
In a mixed integer model, the solution values of the decision variables are 0 or 1.
The simplex method cannot be used to solve quadratic programming problems.
The early start of an activity that has only one predecessor is equal to the early finish of
that predecessor.
A Markov assumption is that the probabilities in each row sum to 1 because they are
mutually exclusive and collectively exhaustive.
The minimax regret criterion minimizes the maximum regret.
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 origin node is constrained by
the supply at that node.
D) all of the above
The Hurwicz criterion is a compromise between the maximax and maximin criteria.
If fixed costs decrease, but variable cost and price remain the same, the break-even
point:
A) decreases.
B) increases.
C) remains the same.
D) may increase or decrease depending on sales.
The steps of the management science process are:
A) problem definition, model construction, observation, model solution,
implementation.
B) observation, problem definition, model construction, model solution,
implementation.
C) model construction, problem definition, observation, model solution,
implementation.
D) observation, implementation, problem definition, model construction, model
solution.
A ________ is an up-and-down repetitive movement that repeats itself over a time span
of more than 1 year.
A) prediction
B) seasonal pattern
C) trend
D) cyclical pattern
________ methods are the most common type of forecasting method for the long-term
strategic planning process.
A) Regression
B) Qualitative
C) Time series
D) Queuing
The interval labeled “D” in the diagram is:
A) production cycle.
B) order receipt period.
C) shipping lead time.
D) inventory fill rate.
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.
How many times will you find more than twenty-one customers either buying a soda or
waiting in line to make that purchase?
A) one in four
B) one in five
C) one in six
D) one in seven
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 transshipment locations are:
A) Madison and Atlanta.
B) Philadelphia and Knoxville.
C) Madison, Atlanta, Philadelphia and Knoxville.
D) Dayton, Bloomington, and Albany.
Consider the following project.
How much can activity F be delayed without delaying the project completion?
A) 1 day
B) 2 days
C) 3 days
D) 4 days
Customers arrive at a music store at an average of 1 per minute (Poisson arrivals). The
service rate is 15 customers per hour (exponential service times). What is the minimum
number of servers needed to keep the waiting time in the system under 5 minutes?
A) 4
B) 5
C) 6
D) 7
A ________ deviational variable is the amount by which a goal level is underachieved.
A) negative
B) positive
C) positive or negative
D) positive and negative
Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M).
Each big shelf costs $500 and requires 100 cubic feet of storage space, and each
medium shelf costs $300 and requires 90 cubic feet of storage space. The company has
$75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet
available for storage. Profit for each big shelf is $300 and for each medium shelf is
$150. If the furniture company purchases no big shelves and 200 medium shelves,
which of the two resources will be completely used (at capacity)?
A) investment money only
B) storage space only
C) investment money and storage space
D) neither investment money nor storage space
A university is planning 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. If we know that 20 people will attend, what price should
be charged per person to break even?
A) $120
B) $150
C) $175
D) $200
The owner of Black Angus Ranch is trying to determine the correct mix of two types of
beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five
essential ingredients are contained in the feed, shown in the table below. The table also
shows the minimum daily requirements of each ingredient.
The constraint for ingredient 3 is:
A) .5A + .75B = 20.
B) .3B = 20.
C) .3B≤ 20.
D) .3B ≥ 20.
Consider the following frequency of demand and random numbers:
Random numbers: 0.13, 0.81, 0.53.
If the simulation begins with the second random number, the simulated value for
demand would be:
A) 1
B) 2
C) 3
D) 4
Figure 2
Consider the optimization problem represented by this graph. Line GH represents the
objective function. Which of the following statements is best?
A) This is a single optimal solution.
B) All points along GH are optimal.
C) All points on lines AB, CD and DE that touch the shaded region are optimal.
D) All points in the shaded region are optimal
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 following pairwise comparison matrix summarizes the
preferences of the plant manager.
Which choice does the decision maker prefer?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred.
The branch and bound method of solving linear integer programming problems is:
A) a nonlinear method.
B) a relaxation method.
C) a graphical solution.
D) an enumeration method.
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 a
linear trend line. His fingers are aching by the time he reaches May and he is worried
about his ability to stuff tacos during tomorrow’s dinner rush. Help him out by finding the
forecast for June.
A) 673.3
B) 628.2
C) 651.4
D) 599.3
The diagram above represents which type of inventory model?
A) Economic Order Quantity (EOQ)
B) EOQ with Noninstantaneous Receipt
C) Economic Production Quantity
D) Fixed Period Model
A firm is currently purchasing an item for inventory using the basic EOQ model. They
plan on making the product themselves and will be using the EOQ model based on
noninstantaneous receipt of inventory. If everything else stays the same, what changes
should the firm expect?
A) EOQ decreases.
B) Average inventory level decreases.
C) Reorder point increases.
D) Safety stock increases.
The slope of the line labeled “B” in the diagram is:
A) rate of inventory demand.
B) production rate.
C) shipping rate.
D) production rate minus rate of inventory demand.
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 the 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 time constraint?
A) 2D + 4R ≤ 480
B) 2R + 3D ≤ 480
C) 3R + 2D ≤ 480
D) 2R + 4D ≤ 480
A transportation table that has a cell evaluation of 0 means that:
A) the table is optimal.
B) an equivalent alternative solution exists.
C) supply and demand are equal.
D) the solution is not optimal.
Figure 2
What is the equation for the constraint AB?
A) 3X + 12Y ≥ 15
B) X + 4Y ≥ 12
C) X + Y ≥ 15
D) 12X +3Y ≥ 36
For the normal distribution, the mean plus and minus 1.96 standard deviations will
include what percent of the observations?
A) 84%
B) 90%
C) 95%
D) 97%
A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will
occur between 2 and 4 times?
A) .2188
B) .4922
C) .6016
D) .8204
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 and they
carry 21 jars for safety stock. If there are 4 jars on the shelf when an order is placed,
how much should the store order?
A) 77
B) 81
C) 32
D) 36
Dinnertime
A professor is planning an informal gathering for 100 or so of his closest friends. The
project breaks down as follows:
What is the fastest this project can be completed?
A) 34
B) 38
C) 44
D) 48
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 4 for this distribution?
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.
What is the nonlinear profit function for the XYZ company? Simplify the terms as
much as possible.
________ techniques provide results that contain uncertainty, unlike mathematical
programming techniques which are deterministic.
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 is the EVPI for this situation?
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 7.
A(n) ________ solution occurs when the number of independent unique assignments
equals the number of rows or columns.
The ________ is a compromise between the maximax and the maximin criterion.
A ________ organizes numerical data to describe the events of an experiment.
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 is interested in developing a series of horse-only paths (named The Caballo
Real) among its points of interest. The horse has a small budget and no one to help her,
so it would prefer to develop those paths using a minimum quantity of materials and
labor. Which of the point to point paths should be used and what is the total distance?
Consider the following transportation problem:
If the optimal solution includes x11 = 100 and x22 = 200, determine the remaining
shipments that will result in a minimum cost of $1700.
Given the nonlinear programming model Max Z = 5x1 – 2x2
2
Subject to: x1 + x2 = 6
What is the optimal profit?
Three time estimates (optimistic, most likely, and pessimistic) provide an estimate of
the mean and variance for each activity, based on the ________ distribution.
The expected value of the standard normal distribution is equal to ________.
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 are the objective function terms that involve the demand locations?
A one-way street in a downtown area should be modeled as a(n) ________ branch in a
maximal flow model.
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 Northwest Corner method, the initial solution would have a total
transportation cost of ________.
Given the following information for a project, what are the estimated slack times (in
weeks) for activities A-H?
CP = Critical Path