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The value of the game is the defensive player's gain and the offensive player's loss in a
zero-sum game.
One aspect of project control is team building.
In a transportation problem, a demand constraint for a specific destination represents
the amount of product demanded by a given destination (customer, retail outlet, store).
Game theory addresses decision situations with two or more decision makers in
competition.
The arrival rate is the frequency at which customers arrive at a waiting line according to
a probability distribution.
The lower the service level, the greater the probability of a stockout.
The method of Lagrange multipliers can only be used in solving nonlinear
programming problems with one equality constraint.
The slope of a curve at its highest point equals 1.
The expected project completion time is assumed to be normally distributed.
The shortest route network problem could help identify the best route for pizza delivery
drivers from the pizza parlor to a specific customer.
Markov analysis does not provide a recommended decision.
A conditional probability is the probability that an event occurs given that another event
has already occurred.
A profit function of Z = 3x2 - 12x + 5 reaches maximum profit at x = 2 units of output.
In implicit enumeration the feasible integer solutions closest to the optimal non-integer
solution are evaluated to see which is best.
The slope of a curve at its highest point equals 0.
Lagrange multiplier is another name for shadow price.
A preference scale assigns numerical values to XOAXOAerent levels of preference.
If we change the constraint quantity to a value outside the sensitivity range for that
constraint quantity, the shadow price will change.
The minimax regret criterion maximizes the minimum regret.
Operating characteristics describe the methods used by the service process.
Rounding non-integer solution values up to the nearest integer value will result in an
infeasible solution to an integer linear programming problem.
Markov analysis is a probabilistic technique.
In a given AHP problem, the consistency index is .15, and the random index is .90. In
this instance, there are probably serious inconsistencies and, therefore, the AHP result
may not be meaningful.
Markov analysis is a descriptive technique that results in probabilistic information.
The objective function always consists of either maximizing or minimizing some value.
A change in the objective function coefficient of a basic variable cannot change the
value of zj for a non-basic variable in the final simplex tableau.
A point of equilibrium is a value that is simultaneously the maximum of a row and the
minimum of a column.
In synthesization, decision alternatives are prioritized within each criterion.
In a transportation problem, the supply constraint represents the maximum amount of
product available for shipment or distribution at a given source (plant, warehouse, mill).
In a multiple-server system, the ratio of the mean effective service rate for the system to
the arrival rate to the system must be greater than 1 for customers to be served in a
reasonable time.
Markov analysis provides information on the probability of customers switching from
one brand to one or more other brands.
Flows in a network can only be in one direction.
The minimax criterion minimizes the maximum payoff.
In a 0-1 integer programming problem involving a capital budgeting application (where
xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if
project 2 is selected, project 1 cannot be selected.
A basic feasible solution satisfies the model constraints and has the same number of
variables with non-negative values as there are constraints.
Seventy-two percent of all observations fall within one standard deviation of the mean
if the data is normally distributed.
The brand-switching problem analyzes the probability of customers' changing brands of
a product over time.
Typically, finding a corner point for the feasible region involves solving a set of three
simultaneous equations.
Which of the following assumptions is not an assumption of the transportation model?
A) Shipping costs are constant.
B) There is only one transportation route between source and destination.
C) There is only one transportation mode between source and destination.
D) Actual supply and actual demand must be equal.
The purpose of break-even analysis is to determine the number of units of a product to
sell that will:
A) appeal to the consumer.
B) result in a profit.
C) result in a loss.
D) result in zero profit.
Taco Quatro
Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients,
cheese, meat, beans and tortillas.
A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla
needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2
ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the
Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa
sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new
Burritaco sells for $4.
The assistant manager checks the cooler one fine Monday morning and sees that they
have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas
on hand.
How many decision variables are in the LP formulation?
A) 1
B) 2
C) 3
D) 4
Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).
Which is the appropriate profit constraint for this scenario?
A) 16R + 24W + 16d2
+ + 24d2
- = 500
B) 16R + 24W + d2
+ + d2
- = 500
C) 16R + 24W + 16d2
+ + 16d2
- + 24d2
+ + 24d2
-= 500
D) 16R + 24W + 16d2
+ + 24d2
- ≥ 500
If t is the expected completion time for a given activity, then:
A) LF = LS - t.
B) EF = ES - t.
C) EF = ES + t.
D) EF = LS - t.
Armed only with his fingers, the owner decides that the safest forecasting approach is a
moving average of two periods. 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) 49.1
B) 44.5
C) 41.2
D) 43.3
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.
It was tough to be optimistic, but the cold, calculating father did exactly that, inspired
by a particularly smooth single malt scotch. Which alternative would be the best choice
given this rare state of optimism?
A) A
B) B
C) C
D) D
Three fast food restaurants on a college campus have been subjected to pairwise
comparisons on the quality of their food. The matrix is:
Which choice does the decision maker prefer?
A) Mama's
B) Papa's
C) Freddie's
D) This cannot be determined from the information provided.
The objective function in a goal programming model seeks to ________ the deviation
from goals in the order of the goal priorities.
A) free
B) even out
C) maximize
D) minimize
A work breakdown structure breaks down a project into:
A) weeks.
B) areas.
C) arcs.
D) modules.
The analytic hierarchy process:
A) optimizes procedures with a single goal.
B) requires no pairwise comparison.
C) uses both qualitative and subjective assessment.
D) does not require the input of a decision maker.
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.
In the process of evaluating location alternatives, the transportation model method
minimizes the:
A) total demand.
B) total supply.
C) total shipping cost.
D) number of destinations.
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. Which of the following is not a feasible purchase combination?
A) 100 big shelves and 82 medium shelves
B) 150 big shelves and 0 medium shelves
C) 100 big shelves and 100 medium shelves
D) 100 big shelves and 0 medium shelves
In the simplex procedure, if it is not possible to select a pivot row, this indicates that:
A) the solution is infeasible.
B) the solution is unbounded.
C) there are multiple optimal solutions.
D) the formulation is incorrect.
Let: rj = regular production quantity for period j, oj =overtime production quantity in
period j, ij = inventory quantity in period j, and dj= demand quantity in period j. Correct
formulation of the demand constraint for a multiperiod scheduling problem is:
A) rj +oj+ i2 - i1 ≥ dj.
B) rj +oj+ i1 - i2 ≥ dj.
C) rj +oj + i1 - i2 ≤ dj.
D) rj -oj- i1 + i2 ≥ dj.
Based on the information in the table, which tasks are least likely to be assigned to a
student?
A) grading
B) scanning
C) copying
D) organizing portfolios
Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).
Which is the appropriate corn constraint for this scenario?
A) 3R + 2W + d3
+ + d3
- ≤ 40
B) 3R + 2W + d3
+ + d3
- ≥ 40
C) 3R + 2W + 3d3
+ + 2d3
- ≤ 40
D) 3R + 2W + d3
+ + d3
- = 40
The Vacation
Final exams are almost here and once they are done, it will be time to reward myself
with a well-deserved vacation. As a state employee, I haven't seen a raise since... well,
ever. Thus an important criterion, in fact the most important criterion is to find an exotic
region that can be visited inexpensively. There are three states of nature that could
impact costs in these five areas of interest, and they correspond to the relative strength
of the US Dollar against that region's dominant currency. Rather than squander my time
doing any actual publishable research, instead I have determined the average cost per
day to visit each region under each of the possible states of nature. This table, which
should not be construed as actual vacation advice, appears below.
What do the regrets look like for Scandinavia from left to right?
A) 0, 21, 24
B) 0, 15, 5
C) 6, 0, 16
D) 5, 0, 12
Donuts Please
The number of donuts needed for department meetings at the start of the semester can
be modeled by the continuous probability distribution , which we can integrate
from 0 to some value x, which is the number of days before the actual beginning of the
semester.
Analogue simulation replaces a physical system with an analogous physical system that
is ________ to manipulate.
A) harder
B) easier
C) equally Difficult
D) more expensive
It was a house with seven cats, four female and three male, and the litterbox was busier
than O'Hare Airport during the week of Thanksgiving. The beleaguered husband's home
office was right around the corner from the laundry room, where the litterbox was kept,
and heard three separate instances of use. What is the likelihood that exactly one of the
instances was the dutiful work of one the male cats?
A) .273
B) .187
C) .419
D) .079
Consider the following project.
Determine the estimated completion time of the project.
A) 23 days
B) 22 days
C) 25 days
D) 20 days
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 ________ multiplies the decision payoff for each state of nature by an equal
weight.
A) dominant decision
B) coefficient of optimism
C) equal likelihood criterion
D) none of the above
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:
v = 1000 - 8p. What is the optimal price of the ball bearings that will maximize the
profit?
A) $47.99
B) $53.99
C) $58.99
D) $63.99
The landlord uses the following scheme for decision variables:
What should the objective function be?
A) Min Z = 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8
B) Min Z = 2700x1 - 400x2 + 2500x3 - 1000x4 + 600x5 - 250x6 + 350x7 - 400x8
C) Max Z = 100x1 + 100x2 + 80x3 + 80x4 + 15x5 + 15x6 + 20x7 + 20x8
D) Max Z = 100x1 - 100x2 + 80x3 - 80x4 + 15x5 - 15x6 + 20x7 - 20x8
In a balanced transportation model where supply equals demand, all constraints are:
A) inequalities.
B) equalities.
C) A and B
D) none of the above
In a noninstantaneous receipt model, daily demand is 55 units and daily production is
120 units, Co = $70 and Cc = $4 per unit per year. What is the maximum inventory
level? (Assume that the facility is open 365 days per year.)
A) 616.9
B) 618.4
C) 620.3
D) 622.9
Assume that x2, x7 and x8 are the dollars invested in three Different common stocks
from New York Stock Exchange. In order to diversify the investments, the investing
company requires that no more than 60% of the dollars invested can be in 'stock 2". The
constraint for this requirement can be written as:
A) x2 ≥ .60.
B) x2 ≥ .60 (x2 + x7 + x8).
C) .4x2 - .6x7 - .6x8 ≤ 0.
D) .4x2 - .6x7 - .6x8 ≥ 0.
A graduate research assistant "moonlights" at the short order counter in the student
union snack bar in the evenings. He is considering asking for help taking orders, but
needs to convince the management that they should hire another student. Because he is
taking a simulation class, he thinks it may be the perfect way to convince management
to hire more help if he can show that customers have to wait a long time. When a
customer arrives, he takes their order and their payment, prepares the food, gives it to
the customer, and then takes the order from the next person in line. If someone arrives
while he's cooking an order, they have to wait until he's completed the current order. He
has simulated 5 orders.
Average utilization is:
A) 67%.
B) 72.5%.
C) 83.4%.
D) 95%.
Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).
Which is the appropriate time constraint for this scenario?
A) 2R + 3W + d2
+ + d2
- = 72
B) 2R + 3W + d1
+ + d1
- ≤ 72
C) 2R + 3W + d1
+ + d1
- = 72
D) 2R + 3W + d2
+ + d2
- ≤ 72
A company has three goals, listed in order of importance.
Achieve a total profit of at least $240 million.
Maintain the current employment level of 3,000 employees
Invest no more than $70 million in capital.
What is the objective function for a goal program for this situation?
A) Min P1d1
- , P2d2
- , P3d3
+
B) Min P1d1
- , P2d2
+ , P2d2
- ,P
3d3
-
C) Min P1d1
- , P2d2
- , P2d2
- ,P
3d3
+
D) Min P1d1
+ , P2d2
- , P2d2
- ,P
3d3
+
________ are good for stable demand with no pronounced behavioral patterns.
A) Longer-period moving averages
B) Shorter-period moving averages
C) Moving averages
D) Weighted moving averages
Consider the following linear program:
MAX z = 5x + 3y
s.t. x - y ≤ 6
x ≤ 1
The optimal solution:
A) is infeasible.
B) occurs where x = 1 and y = 0.
C) occurs where x = 0 and y = 1.
D) results in an objective function value of 5.
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 is the average
inventory if they produce an optimal batch size?
A) 66224
B) 6934
C) 7256
D) 7528
The indicator that results in total revenues being equal to total cost is called the:
A) marginal cost.
B) marginal volume.
C) break-even point.
D) profit mix.
A bakery is considering hiring another clerk to better serve customers. To help with this
decision, records were kept to determine how many customers arrived in 10-minute
intervals. Based on 100 10-minute intervals, the following probability distribution and
random number assignments developed.
Suppose the next three random numbers were .11, .42 and .84. Use these values to
simulate arrivals into the bakery and determine the average number of arrivals per
10-minute period based on these occurrences. The average number of arrivals per
10-minute period is:
A) 6
B) 7
C) 8
D) 9
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 the regression equation resulting from using the month, where January = 1,
February = 2, etc.) to forecast Pounds?
A business analyst describes his company's profit function as 3x2 + 6x - 200. If x is the
output volume, what statements can you make about the price, fixed cost, and variable
cost?
A newly opened bed-and-breakfast projects the following:
Monthly fixed costs $8000
Variable cost per occupied room per night $40
Revenue per occupied room per night $165
How many rooms would have to be occupied per month in order to break even?
The Dean's Office keeps tracks of student complaints received each week. The
probability distribution for complaints can be represented as a table as shown below.
The random variable xirepresents the number of complaints, and p(xi) is the probability
of receiving xi complaints.
What is the probability that they receive less than 3 complaints in a week?
If a nonlinear programming model consists of a single nonlinear objective function and
no constraints, it is called a(n) ________ optimization problem.
The transition matrix below shows the probabilities that customer switch between two
grocery stores, Don's and Limmer's, each week.
If there are 2000 customers who shop at either store, how many over the long run would
shop at Limmer's?
A Markov process has the following transition matrix:
A B
A 0.25 0.75
B 0.60 0.40
What are the steady state probabilities?
The management scientist was planning to leave his actions up to the wisdom of his
model, but before he could press "Solve" on his Excel spreadsheet, his wife weighed in
on the project. This was only reasonable, as it was her house before they tied the knot. It
has been her dream to move back into this cottage once the management scientist goes
to his great reward. She insists that the back door and garage door components of this
project happen. If the variables have been chosen as in the table, construct an objective
function and constraints that meet the management scientist's bride's requests.
In an unbalanced transportation problem, if supply exceeds demand, the shadow price
for at least one of the supply constraints will be equal to ________.
The analytic hierarchy process, scoring models, and goal programming are all
considered to be ________ decision making techniques because they incorporate
decisions based on more than one objective.
Consider the following decision tree.
Which decision, A or B, is best? What is the expected value of this decision?
Figure Delivery Routes
Consider the network diagram given in Figure 1. Assume that the numbers on the
branches indicate the length of cable (in miles) between each pair of the six nodes on a
telecommunication network. What is the minimum number of miles of cable to be used
to connect all six nodes?
Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities
along each branch. Determine the maximal flow from source node 1 to destination node
9.
In an integer program, if building one facility required the construction of another type
of facility, this would be written as: ________.
Consider the curve 7x2 - 14x + 28. What is the highest point on this curve?
In a factory, machines breakdown at an average of 6 machines per hour according to a
Poisson distribution. The time a repair person takes to repair the machine is not defined
by any probability distribution, but has a mean of 8 minutes and a standard deviation of
3 minutes.On average, how long will a machine have to wait before it is fixed?
