1) PERT stands for Probabilistic Evaluation and Review Technique.
2) CPM stands for Comprehensive Project Method.
3) An integer programming solution can never produce a greater profit objective than
the LP solution to the same problem.
4) In a normal distribution, the Z value represents the number of standard deviations
from a value X to the mean.
5) Validation relates to building the right model.
6) Development of a new deluxe version of a particular software product is being
considered. The activities necessary for the completion of this are listed in the table
below (Time in weeks).
(a) What is the project completion date?
(b) What is the total cost required for completing this project on normal time?
(c) If you wish to reduce the time required to complete this project by one week, which
activity should be crashed, and how much will this increase the total cost?
7) The two most common objectives for the assignment problem are the minimization
of
A) uncertainty or inexperience.
B) total costs or inexperience.
C) total costs or total time.
D) total time or inexperience.
E) total costs or uncertainty.
8) Consider the following 0-1 integer programming problem:
If we wish to add the constraint that no more than two of these variables must be
positive, how would this be written?
A) 2X + 2Y + 2Z =< 3
B) X + Y + Z =< 2
C) X =< 2, and Y =< 2, and Z =< 2
D) X, Y, Z =< 2
E) None of the above
9) A solved LP problem indicated that the optimal solution was X1 = 5, X2 = 10, A1 =
40. The first constraint was: 4X1 + 2X2 >= 80. This solution is:
A) indeterminant.
B) degenerate.
C) infeasible.
D) unbounded.
E) None of the above
10) An arrival in a queue that reneges is one who
A) after joining the queue, becomes impatient and leaves.
B) refuses to join the queue because it is too long.
C) goes through the queue, but never returns.
D) jumps from one queue to another, trying to get through as quickly as possible.
E) None of the above
11) Defects in computer hard-drives will usually render the entire computer worthless.
For a particular model, the percent defective in the past has been 1%. If a sample size of
400 is taken, what would the 95.5% lower control chart limit be?
A) 0.00995
B) 0.00005
C) 0.00000
D) 0.01000
E) 0.09550
12) Slack time in a network is the
A) amount of time that an activity would take assuming very unfavorable conditions.
B) shortest amount of time that could be required to complete the activity.
C) amount of time that you would expect it would take to complete the activity.
D) difference between the expected completion time of the project using pessimistic
times and the expected completion time of the project using optimistic times.
E) amount of time that an activity can be delayed without delaying the entire project.
13) Given the following distances between destination nodes, what is the minimum
distance that connects all the nodes?
A) 450
B) 150
C) 350
D) 650
E) None of the above
14) Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival
rate of 16 customers per hour. What is the probability that in the next hour there will be
exactly 8 arrivals?
A) 1.000
B) 0.200
C) 0.175
D) 0.825
E) None of the above
15) If the sale of ice cream and pizza are independent, then as ice cream sales decrease
by 60 percent during the winter months, pizza sales will
A) increase by 60 percent.
B) increase by 40 percent.
C) decrease by 60 percent.
D) decrease by 40 percent.
E) be unrelated.
16) 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
17) Typical resources of an organization include
A) machinery usage.
B) labor volume.
C) warehouse space utilization.
D) raw material usage.
E) All of the above
18) Two models of a product Regular (X) and Deluxe (Y) are produced by a company.
A linear programming model is used to determine the production schedule. The
formulation is as follows:
The optimal solution is X = 100, Y = 0.
How many units of the regular model would be produced based on this solution?
A) 0
B) 100
C) 50
D) 120
E) None of the above
19) At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The
car wash takes exactly 4 minutes (this is constant). On average, how long would each
driver have to wait before receiving service?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
E) None of the above
20) The initial values for the state probabilities
A) are always greater than the equilibrium state probabilities.
B) are always less than the equilibrium state probabilities.
C) do not influence the equilibrium state probabilities.
D) heavily influence the equilibrium state probabilities.
E) None of the above
21) Table 11-5
How long could Table 11-5’s activity F be delayed without delaying the project?
A) 2
B) 3
C) 14
D) 16
E) None of the above
22) A company is considering producing a new children’s bar soap. A market research
firm has told the company that if they perform a survey, a positive survey of a favorable
market occurs 65 percent of the time. That is, P(positive survey £ favorable market) =
0.65. Similarly, 40 percent of the time the survey falsely predicts a favorable market;
thus, P(positive survey £ unfavorable market) = 0.40. These statistics indicate the
accuracy of the survey. Prior to contacting the market research firm, the company’s best
estimate of a favorable market was 50 percent. So, P(favorable market) = 0.50 and
P(unfavorable market) = 0.50. Using Bayes’ theorem, determine the probability of a
favorable market given a favorable survey.
A) 0.62
B) 0.38
C) 0.53
D) 0.65
E) None of the above
23) Given an activity’s optimistic, most likely, and pessimistic time estimates of 3, 5,
and 15 days, respectively, compute the PERT standard deviation for this activity.
A) 2
B) 4
C) 5
D) 15
E) None of the above
24) An air conditioning and heating repair firm conducted a study to determine if the
average outside temperature could be used to predict the cost of an electric bill for
homes during the winter months in Houston, Texas. The resulting regression equation
was:
Y = 227.19 – 1.45X, where Y = monthly cost, X = average outside air temperature
(a) If the temperature averaged 48 degrees during December, what is the forecasted cost
of December’s electric bill?
(b) If the temperature averaged 38 degrees during January, what is the forecasted cost of
January’s electric bill?
25) If two events (A,B) are not mutually exclusive, what is the probability of event A or
event B occurring?
26) Identify three potential problems with people (two with management and one with
the quantitative analysts themselves) that may hinder successful implementation of a
quantitative model.
27) Candy Incorporated stocks bubble gum game cards, an item that has a normally
distributed demand during the reorder period with a mean of 12 dozen boxes and a
standard deviation of two dozen boxes. If it is desirable to experience a stockout only
10 percent of the time, what is the appropriate safety stock?
28) Smalltime Investments Inc. is going to purchase new computers. There are ten
employees, and the company would like one for each employee. The cost of the basic
personal computer with monitor and disk drive is $2,000, while the deluxe version with
VGA and advanced processor is $3,500. Due to internal politics, the number of deluxe
computers should be less than half the number of regular computers, but at least three
deluxe computers must be purchased. The budget is $27,000, although additional
money could be used if it were deemed necessary. All of these are goals that the
company has identified. Formulate this as a goal programming problem.
– = underachievement of goal of 10 computers to purchase
29) Describe the utility curve of a risk seeker.
30) In a four-factor analysis used in a multifactor evaluation process, it is desired to
have the F1 importance weight four times as much as the F2 importance weight. The F2
importance weight should be four times as much as the F3 importance weight. The F3
importance weight should be four times as much as the F4 importance weight.
Determine the appropriate importance weights of F1, F2, F3, F4 to be used in the
multifactor evaluation process. (Hint: Consider numerator factors of 4.)
31) A computer start-up named Pear is considering entering the U.S. market with what
they believe to be a smaller and faster computer than some of the existing products on
the market. They want to get a feel for whether or not customers would be willing to
switch from some of the existing bigger brands to consider their product. They want to
collect a reasonable sample from across the U.S. representative of all age brackets.
They have split the United States into 2 regions: East and West. They want at least 65%
of their sample to cover the East and no fewer than 25% of the West. They also have
divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at
least 50% of their sample to be between 18-35 and at least 40% to be between 36-69.
The costs per person surveyed is given in the table below:
Assume that at least 1,000 people are to be surveyed. The problem is for Pear Company
to decide how many people to survey from each age bracket within each region in order
to minimize costs while meeting requirements. Find the optimal solution and minimum
cost.
32) Henry has a newspaper stand where he sells papers for $0.50 each. The papers cost
him $0.30 each, giving him a 20-cent profit on each one he sells. From past experience,
Henry knows that
20% of the time he sells 100 papers
20% of the time he sells 150 papers
30% of the time he sells 200 papers
30% of the time he sells 250 papers
Assuming that Henry believes the cost of a lost sale is 10 cents and any unsold papers
cost him $0.30, simulate Henry’s profit outlook over 5 days if he orders 175 papers for
each of the 5 days. Use the following random numbers: 52, 06, 50, 88, 53.
33) Discuss why it is sometimes prudent not to order the minimum level required to
obtain a quantity discount.