課程教師︰張錦特
課程性質：國企系必選
開課學院：管理學院
開課系所︰國企系
考試日期（年月日）︰96/11/9
考試時限（分鐘）：90
是否需發放獎勵金：是
試題 :
1. The Boston South Fifth Street Softball League consists of three teams:
Mama's Boys, team 1; the Killers, team 2; and the Machos, team 3.
Each team plays the other teams just once during the season. The win-loss
record for the past five years is as follows:
WINNER (1) (2) (3)
Mama's Boys(1) X 3 4
The Killers(2) 2 X 1
The Machos(3) 1 4 X
Each row represents the number of wins over the past five years.
Mama's Boys beat the Killers 3 times, beat the Machos 4 times, and so on (12%)
(a) What is the probability that the Killers win every game next year?
(b) What is the probability that the Machos will win at least one game
next year?
(c) What is the probability that the Mama's Boys will win exactly one
game next year?
(d) What is the probability that the Killers will win less than 2 games
next year?
2. Kenneth Brown is the principal owner of Brown oil, inc. After quitting his
university teaching job, Ken has been able to increase his annual salary by a
factor of over 100. At the present time, Ken is forced to consider purchasing
some more equipment for Brown Oil because of competition. His alternatives
are shown in the following table: (9%)
EQUIPMENT FAVORABLE MARKET UNFAVORABLE MARKET
sub100 300,000 -200,000
Oiler J 250,000 -100,000
Texan 75,000 -18,000
For example, if Ken purchases a sub 100 and if there is a favorable market,
he will realize a profit of $300,000. On the other hand, if the market is
unfavorable, Ken will suffer a loss of $200,000. But Ken has always been a
very optimistic decision maker.
(a) What type of decision is Ken facing?
(b) What decision critetion should he use?
(c) What alternative is the best?
3. The Lubricant is an expensive oil newsletter to which many oil giants
suscribe, including Ken Brown (see prob.2 for details). In the last issue,
the letter describe how the damend for oil products would extremely high.
Apparently, the American consumer will continue to use oil products even
if the price of these product doubles. Indeed, one of the articles in the
Lubricant states that the chances of a favorable market for oil products
was 70% ; while the chance of an unfavorable mkt is 30%. Ken would like to
use these probabilities in determining the best decision. (9%)
(a) What decision model should be used?
(b) What is the optimal decision?
(c) Ken believes that the $300,000 figure for the sub100 with a favorable mkt
is too high. How much lower would this figure have to be for Ken to change his
decision made in part b?
4. Students in a management science class have just received their grades
on the first test. The instructor has provided the information about the
first test grades in some previous classes as well as the final average for
the same students. Some of these grades have been sample and are as follows:
(15%)
STUDENT 1 2 3 4 5 6 7 8 9
1st test grade 98 77 88 80 96 61 66 95 69
Final average 93 78 84 73 84 64 64 95 76
(a) develop a regression model that could be used to predict the final average
in the cource based on the first test grade.
(b) predict the final average of a student who made an 83 on the first test.
(c) give the values of r and r^2 for this model. Interprete the value of
r^2 in the context of this problem.
5. Data collected on the yearly demand for 50-pound of fertilizer at Wallace
Garden Supply are shown in the following table. Develop a three-year moving
average to forcast sales. Then estimate demand again with a weighted moving
average in which sales in the most recent year are given a weigth of 2 and
sales in the other 2 years are each given a weight of 1. Which method do you
think is best? (10%)
YEAR DEMAND FOR FERTILIZER(1,000 OF BAGS)
1 4
2 6
3 4
4 5
5 10
6 8
7 7
8 9
9 12
10 14
11 15
6. Let us consider the following example that decision makers wish to assign
two-side S-shaped penalty to an objective distant from the predefined interval
goal.
Goal: Zij(X)+n1-p1=[100, 110]
Constrants: X 屬於 F (F is a feasible set)
Table 1. Penalty scales for the attribute is listed below.
____________________________
Unit(%) Marginal penalty
----------------------------
Below85 0.8
85-90 2
90-100 1
100-110 0
110-120 1
120-125 2
over125 0.8
____________________________
where Zij(X) (j=1,2,3) is the linear function of x1............xn;
n1 and p1 are, respectively, under- and over-achievement if target
interval[100, 110]. As can be seen in Table 1, these penalty scales imply to
representing two-side S-shaped penalty function as shown in Figure 1.
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