1) On a practical noteif we are using waiting line analysis to study cars passing through
a single tollbooth, reneging is probably not an issue.
2) One of the major advantages of simulation is “time compression,” i.e., the ability to
study in a relatively short period, activities that would, in reality, take place over a
period of days, months, or even years.
3) Because slack variables yield no profit, they are not included in the objective
function when creating the initial simplex tableau.
4) If a bucket has three black balls and seven green balls, and we draw balls without
replacement, the probability of drawing a green ball is independent of the number of
balls previously drawn.
5) The constraint X1 + X2 =< 1 with 0 -1 integer programming allows for either X1 or
X2 to be a part of the optimal solution, but not both.
6) One of the assumptions of LP is “proportionality.”
7) An n x m matrix, when added to an m x n matrix (n m), yields an n x n matrix.
8) Given two statistically independent events (A,B), the joint probability of P(AB) =
P(A) + P(B).
9) Optimistic decision makers tend to
A) magnify favorable outcomes.
B) ignore bad outcomes.
C) discount favorable outcomes.
D) A and B
E) B and C
10) A set of logical and mathematical operations performed in a specific sequence is
called a(n)
A) complete enumeration.
B) diagnostic analysis.
C) algorithm.
D) objective.
E) None of the above
11) A TIME SERIES forecasting model in which the forecast for the next period is the
actual value for the current period is the
A) Delphi model.
B) Holt’s model.
C) nave model.
D) exponential smoothing model.
E) weighted moving average.
12) There are three items (A, B, and C) that are to be shipped by air. The weights of
these are 4, 5, and 3 tons, respectively. The profits (in thousands of dollars) generated
by these are 3 for A, 4 for B, and 2 for C. There are four units of each available for
shipment. Only 12 tons may be loaded on the plane. The maximum possible profit for
this would be
A) 7.
B) 8.
C) 9.
D) 10.
E) None of these
13) A package express carrier is considering expanding the fleet of aircraft used to
transport packages. Of primary importance is that there is a total of $350 million
allocated for purchases. Two types of aircraft may be purchased – the C1A and the C1B.
The C1A costs $25 million, while the C1B costs $18 million. The C1A can carry 60,000
pounds of packages, while the C1B can only carry 40,000 pounds of packages. Of
secondary importance is that the company needs at least 10 new aircraft. It takes 150
hours per month to maintain the C1A, and 100 hours to maintain the C1B. The least
level of importance is that there are a total of 1,200 hours of maintenance time available
per month.
(a) First, formulate this as an integer programming problem to maximize the number of
pounds that may be carried.
(b) Second, rework the problem differently than in part (a) to suppose the company
decides that what is most important to them is that they keep the ratio of C1Bs to C1As
in their fleet as close to 1.2 as possible to allow for flexibility in serving their routes.
Formulate the goal programming representation of this problem, with the other three
goals having priorities P2, P3, and P4, respectively.
d1
+ = overachievement of ratio of C1B to C1A
14) Mark Achin sells 3,600 electric motors each year. The cost of these is $200 each,
and demand is constant throughout the year. The cost of placing an order is $40, while
the holding cost is $20 per unit per year. There are 360 working days per year and the
lead-time is 5 days. If Mark orders 200 units each time he places an order, what would
his average inventory be (in units)?
A) 100
B) 200
C) 60
D) 120
E) None of the above
15) The R-chart would be useful when we
A) took a number of measurements and computed the average.
B) took a number of measurements and computed the ranges.
C) found the fraction of the production lot defective.
D) found the number of defective items in a production lot.
E) None of the above
16) Table 8-6
The following is a linear programming formulation of a labor planning problem. There
are four overlapping shifts, and management must decide how many employees to
schedule to start work on each shift. The objective is to minimize the total number of
employees required while the constraints stipulate how many employees are required at
each time of day. The variables X1 – X4 represent the number of employees starting
work on each shift (shift 1 through shift 4).
According to Table 8-6, which describes a labor planning problem and its solution, how
many workers would be assigned to shift 1?
A) 12
B) 13
C) 0
D) 2
E) None of the above
17) Table 12-5
According to the information provided in Table 12-5, which presents the solution for a
queuing problem with a constant service rate, what percentage of available service time
is actually used?
A) 0.217
B) 0.643
C) 0.321
D) 0.179
E) None of the above
18) The first step in the maximal-flow technique is to
A) pick the node with the maximum flow.
B) pick any path with some flow.
C) eliminate any node that has a zero flow.
D) add a dummy flow from the start to the finish.
E) None of the above
19) Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school.
Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive
independently and randomly throughout the day at a rate of 1 dog every 4 minutes,
according to a Poisson distribution. Also assume that Sam’s vaccinating times are
exponentially distributed.
(a) Find the probability that Sam is idle.
(b) Find the proportion of time that Sam is busy.
(c) Find the average number of dogs receiving or waiting to be vaccinated.
(d) Find the average number of dogs waiting to be vaccinated.
(e) Find the average time a dog waits before getting vaccinated.
(f) Find the average amount (mean) of time a dog spends between waiting in line and
getting vaccinated.
20) In assigning random numbers in a Monte Carlo simulation,
A) it is important to develop a cumulative probability distribution.
B) it is important to use a normal distribution for all variables simulated.
C) it is not important to assign probabilities to an exact range of random number
intervals.
D) All of the above
E) None of the above
21) The computer monitoring of tracking signals and self-adjustment is referred to as
A) exponential smoothing.
B) adaptive smoothing.
C) trend projections.
D) trend smoothing.
E) running sum of forecast errors (RFSE).
22) Consider the following linear program:
(a) Solve the problem graphically. Is there more than one optimal solution? Explain.
(b) Are there any redundant constraints?
23) Bagles RUS is expanding into a high-growth suburban area. To promote business
and lure customers from the competing Wer Bagel store, they are considering offering a
free dozen bagels to the first 50 customers or radio advertisement. The payoff for
Bagels RUS is given in the table below. What is Bagels RUS’ (X) best strategy?
A) X1
B) X2
C) Y1
D) Y2
E) None of the above
24) The random error in a regression equation
A) is the predicted error.
B) includes both positive and negative terms.
C) will sum to a large positive number.
D) is used to estimate the accuracy of the slope.
E) is maximized in a least squares regression model.
25) A widely used mathematical programming technique designed to help managers and
decision making relative to resource allocation is called
A) linear programming.
B) computer programming.
C) constraint programming.
D) goal programming.
E) None of the above
26) “The probability of event B, given that event A has occurred” is known as a
________ probability.
A) continuous
B) marginal
C) simple
D) joint
E) conditional
27) A market research survey is available for $5,000. Using a decision tree analysis, it is
found that the expected monetary value with no survey is $49,000. If the expected value
of sample information is -$4,000, what is the expected monetary value with the survey?
28) List four significant inventory costs.
29) Identify some possible problems in the quantitative analysis approach.
30) Two factors are considered essential to the selection of blue cheese for the
Burgerhoff Restaurant color and texture. The Burgerhoff insists that color is four times
as important as is texture for food presentation purposes. The Burgerhoff is considering
two brands of blue cheese. After tasting the two brands, color and texture ratings have
been assigned as indicated. Use a multifactor evaluation process to determine which
brand of cheese best suits the needs of the Burgerhoff.
31) Jack Spratt makes candlesticks. His fixed cost is $5,000, variable cost is $3.50, and
selling price, $8.50. To what value must he reduce his variable cost if he wants a
break-even point of 900 units?
32) Explain the purpose of ABC analysis.
33) Explain what is meant by operational gaming and give one example.
34) As part of the planning for a major office development project, it is necessary to
install telephone line to the buildings. Information about the project is given below. The
distances are provided in hundreds of feet. Which offices should be connected so that
total wiring costs (i.e., total distance) are minimized? What is the total length of this?