1) There is no general method for solving all nonlinear problems.
2) In a maximization problem, the Cj – Zj row gives the net loss from introducing one
unit of each variable into the solution.
3) In goal programming, if all the goals are achieved, then the value of the objective
function will always be zero.
4) If a linear programming problem has alternate solutions, the order in which you enter
the constraints may affect the particular solution found.
5) A bank with a single queue to move customers to several tellers is an example of a
single-channel system.
6) Another name for a dummy variable is a binary variable.
7) The decision theory processes of maximizing expected monetary value (EMV) and
minimizing expected opportunity loss (EOL) should lead us to choose the same
alternatives.
8) The term surplus is associated with constraints.
9) Dynamic programming can be applied to a professional tennis player’s serving
strategy.
10) Table 10-5
Final Integer Solution: Z = 208
Table 10-5 represents a solution for an integer programming problem. If one uses the
optimal solution presented, how much slack is there in the first equation?
A) 0 units
B) 5 units
C) 3 units
D) 2 units
E) None of the above
11) Find the shortest route from Node 1 to Node 6.
A) total distance = 350
B) total distance = 410
C) total distance = 270
D) total distance = 520
E) None of the above
12) Cars arrive at a parking lot entrance at the rate of 20 per hour. The average time to
get a ticket and proceed to a parking space is two minutes. There are two lot attendants
at the current time. The Poisson and exponential distribution appear to be relevant in
this situation.
(a) What is the probability that an approaching auto must wait?
(b) What is the average waiting time?
(c) What is the average number of autos waiting to enter the garage?
13) A pairwise comparison rating of 9 means that the two alternatives are
A) equally preferred.
B) moderately preferred.
C) strongly preferred.
D) very strongly preferred.
E) extremely preferred.
14) A capital budgeting problem involving the selection of possible projects under
budget constraints is solved by which of the following?
A) mixed-integer programming
B) 0-1 integer programming
C) goal programming
D) nonlinear programming
E) pure integer programming
15) Fast Service Store has maintained daily sales records on the various size “Cool
Drink” sales.
Assuming that past performance is a good indicator of future sales,
(a) What is the probability of a customer purchasing a $1.00 “Cool Drink?”
(b) What is the probability of a customer purchasing a $1.25 “Cool Drink?”
(c) What is the probability of a customer purchasing a “Cool Drink” that costs greater
than or equal to $1.00?
(d) What is the expected value of a “Cool Drink”?
(e) What is the variance of a “Cool Drink”?
16) The number of cell phone minutes used by high school seniors follows a normal
distribution with a mean of 500 and a standard deviation of 50. What is the probability
that a student uses more than 580 minutes?
A) 0.152
B) 0.0548
C) 0.848
D) 0.903
E) None of the above
17) An integer programming (minimization) problem was first solved as a linear
programming problem, and the objective function value (cost) was $253.67. The two
decision variables (X, Y) in the problem had values of X = 12.45 and Y = 32.75. If there
is a single optimal solution, which of the following must be true for the optimal integer
solution to this problem?
A) X = 13 Y = 33
B) X = 12 Y = 32
C) The objective function value must be less than $253.67.
D) The objective function value will be greater than $253.67.
E) None of the above
18) Which of the following is an applicable characteristic in using the stepping-stone
method?
A) Only an unoccupied square may be used as a ‘stepping-stone.”
B) Only an occupied square may be used as a ‘stepping-stone.”
C) Only the column and row with the highest factory capacity may be used as a
‘stepping-stone.”
D) All of the above
E) None of the above
19) The value of the determinant is
A) ab – cd.
B) ac – bd.
C) ab + cd.
D) ac + bd.
E) ad – cb.
20) Find the shortest route from Node 1 to Node 5.
A) 200
B) 350
C) 250
D) 450
E) None of the above
21) Which of the following scenarios would require simulation for a queuing model?
A) Poisson arrival process
B) exponential service time
C) deterministic arrival process
D) deterministic service time
E) None of the above
22) A primal linear programming problem has four variables and three constraints. The
dual of this will have
A) four variables and three constraints.
B) three variables and four constraints.
C) four variables and seven constraints.
D) seven variables and four constraints.
E) None of the above
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 Wer Bagels’ (Y) best strategy?
A) X1
B) X2
C) Y1
D) Y2
E) None of the above
24)
A)
B)
C)
D)
E) None of the above
25) The value of the determinant is
A) 6243.
B) 24.
C) 15.
D) 10.
E) None of the above
26) Table 14-4
Cuthbert Wylinghauser is a scheduler of transportation for the state of Delirium. This
state contains three cities: Chaos (C1), Frenzy (C2), and Tremor (C3). A transition
matrix, indicating the probability that a resident in one city will travel to another, is
given below. Cuthbert’s job is to schedule the required number of seats, one to each
person making the trip (transition), on a daily basis.
Using the data given in Table 14-4, how many seats should Cuthbert schedule for travel
from Chaos to Tremor for tomorrow?
A) 80
B) 70
C) 20
D) 60
E) None of the above
27) If we wish to monitor the number of defects on a page in a printing process, the
distribution we base our statistics on is the ________ distribution.
28) As part of the planning for a major office development project, it is necessary to
install telephone lines 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?
29) The number of cars arriving at a self-service gasoline station during the last 50
hours of operation are as follows:
Create an appropriate table of interval of random numbers.
30) A water company is analyzing the flow of water through pipes in an office building.
The flow capacities are given in the table below. Flow is measured in 100 gallons/hour.
What is the maximal flow of water from node 1 to node 5?
31) A package express carrier is considering expanding the fleet of aircraft used to
transport packages. There is a total of $220 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. The company needs at least eight new
aircraft. In addition, the firm wishes to purchase at least twice as many C1Bs as C1As.
Formulate this as an integer programming problem to maximize the number of pounds
that may be carried.
32) Ivana Miracle wishes to invest up to her full inheritance of $300,000, and her goal
is to minimize her risk subject to an expected annual return of at least $30,000. She has
decided to invest her money in any of three possible waysCDs, which pay a guaranteed
6 percent; stocks, which have an expected return of 15 percent; and a money market
mutual fund, which is expected to return 8 percent. Risk factors are 1.0 for the CDs, 3.6
for the stocks, and 1.8 for the money market fund. What is the optimal solution and
minimum risk value?
33) First Securities, Inc., an investment firm, has $380,000 on account. The chief
investment officer would like to reinvest the $380,000 in a portfolio that would
maximize return on investment while at the same time maintaining a relatively
conservative mix of stocks and bonds. The following table shows the investment
opportunities and rates of return.
The Board of Directors has mandated that at least 60 percent of the investment consist
of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no
more than 15 percent High Tech Stock. Formulate this portfolio selection problem using
linear programming.