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In a balanced transportation model, supply equals demand such that all constraints can
be treated as equalities.
In a transportation problem, a demand constraint (the amount of product demanded at a
given destination) is a less-than-or equal-to constraint (≤).
Dependent demand items are final products demanded by an external customer.
It's often Difficult to validate that the results of a simulation truly replicate reality.
Random numbers generated by a mathematical process instead of a physical process are
pseudorandom numbers.
Rounding non-integer solution values up to the nearest integer value can result in an
infeasible solution.
The simplex method is a general mathematical solution technique for solving nonlinear
programming problems.
In an unbalanced transportation problem, if demand exceeds supply, the optimal
solution will be infeasible.
Correlation measures the strength of relationship between the x and y variables and the
closer it is to 1 or -1, the greater the proof that the level of x determines the level of y.
Determining the production quantities of Different products manufactured by a
company based on resource constraints is a product mix linear programming problem.
In a 0-1 integer model, the solution values of the decision variables are 0 or 1.
A state of nature is an actual event that may occur in the future.
The last step in solving a linear programming model manually with the simplex method
is to convert the model into standard form.
The multiple-server system models have been developed on the assumption that the
service times are normally distributed.
If an integer linear programming problem has no feasible solution, then its relaxed
solution (LP relaxation) must also have no feasible solution.
Regression is used to relate one variable to one or more variables.
The sensitivity range for a constraint quantity value is the range over which the shadow
price is valid.
Variable costs depend on the number of items produced.
An assignment problem that involves 6 machines to be assigned to 4 workers cannot be
solved using the assignment problem solution procedure described.
An inspector correctly identifies defective products 90% of the time. For the next 10
products, the probability that he makes fewer than two incorrect inspections is 0.736.
In goal programming, problems cannot have two or more goals at the same priority
level.
In a strategy it is assumed that the payoff table is known to all players.
The service rate is the average time it takes to serve a customer.
A long period of real time can be represented by a short period of simulated time.
A consistency index measures the degree of inconsistency in pairwise comparisons.
Branch and bound cannot be used to solve mixed integer programs.
An assignment problem is a special form of transportation problem where all supply
and demand values equal 1.
A conditional probability is the probability that two events will occur simultaneously.
Additional information is used to alter the marginal probability of occurrence of an
event in Bayesian analysis.
A network is an arrangement of paths connected at various points through which items
move.
If an activity cannot be delayed without affecting the entire project, then it is a
________ activity.
A) completed
B) critical
C) crashed
D) normal
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.
If the probability of brisk business is .40 and for slow business is .60, the expected
value of perfect information is:
A) 12
B) 55
C) 57
D) 69
The ________ step in solving a linear programming model manually with the simplex
method is to convert the model into standard form.
A) first
B) second
C) last
D) only
A table of random numbers must be:
A) in descending order.
B) efficiently generated.
C) normally distributed.
D) in ascending order.
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.
If the second goal was to produce no more than 80 units of product two, the objective
function would be:
A) Min P1d1
- + P1d2
-, P2d3
-.
B) Min P1d1
+ + P1d2
-, P2d3
-.
C) Min P1d1
- + P1d2
+, P2d3
-.
D) Min P1d1
- + P1d2
-, P2d3
+.
Napoleon is contemplating four institutions of higher learning as options for a Masters
in Business Administration. Each university has strong and weak points and the demand
for MBA graduates is uncertain. The availability of jobs, student loans, and financial
support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and
Seattle University have comparatively high tuition, which would necessitate Napoleon
take out student loans resulting in possibly substantial student loan debt. In a tight
market, degrees with that cachet might spell the difference between a hefty paycheck
and a piddling unemployment check. Northeastern State University and Texas Tech
University hold the advantage of comparatively low tuition but a more regional appeal
in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist
with the decision. Together they forecast three possible scenarios for the job market and
institutional success and predict annual cash flows associated with an MBA from each
institution. All cash flows in the table are in thousands of dollars.
Under which criterion is Northeastern State University the optimal decision?
A) maximax
B) maximin
C) minimax regret
D) equally likely
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.
Which of these is the money constraint for this scenario?
A) 7X1 + 5X2 + 6X3≤ 10,000
B) 3X1 + 2X2 + 4X3≤ 5,000
C) 6X1 + 4X2 + 7X3≤ 15,000
D) X1 = 200 - 2.25p1
A crew of mechanics at the Department of Transportation garage make minor repairs to
snowplows during the winter. The snowplows break down at an average rate of 4
vehicles per day and breakdowns are distributed according to the Poisson distribution.
The mechanic can service an average of 7 vehicles per day with a repair time
distribution that approximates a negative exponential distribution. Assume an 8 hour
day.
What is the expected average number of snowplows in the garage (waiting for repair
and being repaired)?
A) 1
B) 1.33
C) 2
D) 2.52
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.
Which constraint is appropriate for this scenario?
A) DI + DP + DQ + DC + DL + DM = 2
B) SI + GI + TI + DI ≤ 6
C) SM + GM + TM + DM ≥ 1
D) SI + SP + SQ + SC + SL + SM ≤ 3
The difference between the assignment and the transportation problem is that:
A) each supply and demand value is 1 in the assignment problem.
B) total supply must equal total demand in the transportation problem.
C) the number of origins must equal the number of destinations in the transportation
problem.
D) all of the above
A portion of the variable cells section of the sensitivity report in Excel appears in the
table below. How many potential customers will be reached by the optimal advertising
campaign?
A) 76
B) 8,900
C) 42,080
D) cannot be determined from the sensitivity report
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 model for this problem has how many constraints?
A) 3
B) 4
C) 6
D) 7
________ is a measure of the dispersion of random variable values about the expected
value or mean.
A) Standard deviation
B) Sample mean
C) Population mean
D) Expected value
A frequency distribution is an organization of ________ data about the events in an
experiment.
A) quantitative
B) integer
C) qualitative
D) unknown
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.
Yowzah receives a frantic call from company C. Evidently the fixed cost they quoted
was in rupees rather than dollars. If the current exchange rate is 60 rupees to the dollar,
what is the net effect of an updated analysis?
A) Company C is the bidder of choice throughout the range depicted in the graph.
B) Company C has the highest total cost throughout the range depicted in the graph.
C) Company C has the highest fixed cost of all four companies.
D) Even beyond the range depicted in the graph, company C would be the bidder of
choice.
The simplex method is a general mathematical solution technique for solving ________
programming problems.
A) integer
B) non-linear
C) linear
D) A, B, and C
At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for
purists that can't afford their own. The rental process for these cues is exhaustive and
takes an hour and a half for each application. There are three leasing agents that conduct
these interviews, and on average, it is one hour between customer arrivals.What is the
likelihood there are more than three customers in the system?
A) 12%
B) 24%
C) 76%
D) 88%
In a transportation problem, items are allocated from sources to destinations at a
________ cost.
A) maximum
B) minimum
C) high
D) low
The critical path is the ________ path through the network.
A) longest
B) shortest
C) straightest
D) most expensive
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 annual carrying cost?
A) 1059.03
B) 1355.55
C) 296.51
D) 495.74
Inventory costs include:
A) carrying costs.
B) ordering costs.
C) shortage costs.
D) all of the above
The slope of a curve at its highest point equals:
A) 0
B) 1
C) 2
D) 3
The Lagrange multiplier is:
A) the shadow price for the constraint coefficients.
B) valid over a range of changes in the RHS.
C) the rate of change in the objective value as the RHS of the constraint increases.
D) the minimum threshold for decision variables to enter the solution.
Which of these statements about the sensitivity report is best?
A) There are no Burritacos being made.
B) If the Nacholupa has a cost reduction of more than 0, none will be made.
C) The company can make up to 1E+30 Burritacos.
D) The company can make an additional 0.25 Nacholupas if they want to with the
leftover ingredients.
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
A) trend only
B) trend plus seasonal
C) trend plus random
D) seasonal only
At the break-even point:
A) total revenue equals total cost.
B) profit is maximized.
C) revenue is maximized.
D) costs are minimized.
A required step in the analytic hierarchy process is to determine the:
A) number of hierarchies to use.
B) relative importance of a set of features based on a criterion.
C) goals to be satisfied.
D) expected value of the criteria.
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.
What is the equation for generating x given the random number r?
A) - 2
B) er - 2
C) ln( ) - 2
D) ln(r) - 2
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 sixty six weeks and a standard deviation of ten weeks. The
next career begins on Monday; what is the likelihood that it endures for less than one
year?
A) 14%
B) 12%
C) 10%
D) 8%
Copied below is a portion of the answer report that shows the status of the variable cells
related to the faculty assignment. Which of these statements is consistent with the
answer report?
A) Geoff is assigned to teach Introduction to Operations.
B) Tim is assigned to teach two courses.
C) David is assigned to teach Introduction to Operations
D) Saba is assigned to teach two courses.
Consider the curve 7x2 - 14x + 28. What is the slope at x = 5?
Consider the following network, which shows the location of various facilities within a
youth camp and the distances (in tens of yards) between each facility.
The camp nurse is stationed at Facility B. What is the shortest route from B to C?
The distance formula of d = will find the ________ distance
between two locations.
A graphical solution is limited to solving linear programming problems with ________
decision variables.
When viewing a plot of inventory level against time, the distance on the time axis from
when an order has been placed to when it is received is ________.
The daily demand for a product is normally distributed with a mean of 80 and a
standard deviation of 8. Constant lead time is 4 days. The cost of placing an order is
$20. The item costs $8 and the carrying rate per year is 10% of the item cost. Determine
the reorder point to satisfy 90% of the orders.
The poultry farmer decided to make his own chicken scratch by combining alfalfa and
corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs
$200. The farmer's chickens have a minimum daily requirement of vitamin K (500
milligrams) and iron (400 milligrams), but it doesn't matter whether those elements
come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of
vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of
vitamin K and 50 milligrams of iron. Formulate the linear programming model for this
situation.
Min Z = $4005C + $200A
Subject to: 150C + 250A ≥ 500
75C + 50A ≥ 400
C, A ≥ 0
The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they
sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special
blend. Develop an objective that maximizes profit.
The ________ is a measure of the decision makers optimism.
Vogel's approximation method allocates to the minimum cost cell in the row or column
with the ________ penalty cost.
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
What is the 3-month moving average forecast for January?
One problem with multiple regression is ________, which is a measure of the amount
of "overlapping" information about the dependent variable that's provided by several
independent variables.
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 prêt-à-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.
Help Mondo make the best choice of outfit for each model using linear programming.
________ costs and ________ costs react inversely to each other in response to an
increase in order size.
Inventory ________ costs include storage cost and the cost of capital.
________ model is a method for determining an initial solution for a transportation
problem based on the concept of penalty cost or regret.
The objective function of a diet problem is usually to ________ subject to nutritional
requirements.
The injection molding department of Alver Inc. uses an average of 40 pounds of a
special powder per day. The plant operates 250 days per year. The daily usage of the
powder is normally distributed with a standard deviation of 5 pounds per day. The lead
time to obtain the powder from a supplier is 9 days. The annual holding cost is $2 per
unit and the cost of ordering the powder is $50.
How many units should Alver Inc. order in order to minimize annual ordering and
carrying cost?
When applying linear programming models to project crashing, the objective is to
minimize ________.
