Problem 1. What is the expected value of the following:
X = 1, 2, 3, 4, & 5 and P(X) = 0.01, 0.02, 0.03, 0.04, 0.05, respectively.
a. 0.15
b. 0.00225
c. 0.555
d. None of the above
Problem 2. At a university with 1,000 business majors, there are 200 business students who are enrolled in an introductory statistics course. Of 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students who are enrolled in accounting but are not enrolled in statistics. If a business student is selected at random, what is the probability that the student is not enrolled in accounting?
a. 0.20
b. 0.25
c. 0.30
d. 0.50
e. None of the above
Problem 3. Demand for iPODs has increased steadily over the past 5 months.
Using exponential smoothing with the smoothing constant = 0.3, calculate the forecast for month 6.
|
Month
|
iPODs
|
Forecast
|
|
1
|
60
|
56
|
|
2
|
62
|
|
|
3
|
67
|
|
|
4
|
70
|
|
|
5
|
75
|
|
|
6
|
?
|
|
What is the forecast for month 6?
a. 68.8
b. 76
c. 67.2
d. none of the above.
Problem 4. The annual demand for a product is 1,000 units. The company orders 200 units each time an order is placed. The lead time is 6 days, and the company has determined that 20 units should be held as a safety stock. There are 250 working days per year. What is the reorder point?
a. 20
b. 24
c. 44
d. 120
e. none of the above
Problem 5. 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:
Maximize profit = 50X + 60 Y
Subject to: 8X + 10Y £ 800 (labor hours)
X + Y £ 120 (total units demanded)
4X + 5Y £ 500 (raw materials)
all variables ³ 0
The optimal solution is X = 100 Y = 0.
How many units of the raw materials would be used to produce this number of units?
a. 400
b. 200
c. 500
d. 120
e. none of the above
Problem 6. The following forecasting model has been developed:
^
Y = 36 + 4.3X
Where
Yˆ = demand for air conditioners
X1 = outside temperature ( o F)
What is the demand for air conditioners when the temperature is 70 degrees Fahrenheit?
a. 360
b. 403
c. 66
d. 337
Problem 7. Bus and subway ridership is believed to be related to the number of tourists.
These are the data for the past 12 years:
|
Year
|
Number of Tourists (in 1,000,000s)
|
Ridership (in 1,000,000s)
|
|
1
|
7
|
15
|
|
2
|
2
|
10
|
|
3
|
6
|
13
|
|
4
|
4
|
15
|
|
5
|
14
|
25
|
|
6
|
15
|
27
|
|
7
|
16
|
24
|
|
8
|
12
|
20
|
|
9
|
14
|
27
|
|
10
|
20
|
44
|
|
11
|
15
|
34
|
The regression model that reflects the relationship of the tourists to ridership is:
a. Yˆ = 8.0 + 17.5 X
b. Yˆ = 7.2 + 2.1 X
c. Yˆ = 5.060 + 1.593 X
d. none of the above
Problem 8. For the problem in #7 above, what is the expected ridership if 10 million tourists visit the city?
a. 5.06 million
b. 2.1 million
c. 23 million
d. 20.99 million
Problem 9. Find the shortest route from Node 1 to Node 5 using the shortest route technique.
|
From Node
|
To Node
|
Distance
|
|
1
|
2
|
200
|
|
1
|
3
|
150
|
|
2
|
3
|
50
|
|
2
|
4
|
300
|
|
3
|
4
|
250
|
|
3
|
5
|
200
|
|
4
|
5
|
150
|
a. 350
b. 400
c. 450
d. 600
e. none of the above
Problem 10. Consider a project that has an expected completion time of 60 weeks and a standard deviation of five weeks. What is the probability that the project is finished in 70 weeks or less (round to two decimals)?
a. 0.98
b. 0.48
c. 0.50
d. 0.02
e. none of the above
Problem 11. Customers enter the waiting line at a cafeteria on a first come, first served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is six per minute and the average service rate of a single server is eight per minute, what is the average number of customers in the system?
a. 0.50
b. 0.75
c. 2.25
d. 3.00
e. none of the above
Problem 12. What is the minmax regret decision with the following payoffs depending on the market?
|
Alternative
|
Good Market
|
Fair Market
|
Poor Market
|
|
Single unit
|
25,000
|
20,000
|
-5,000
|
|
Duplex
|
80,000
|
30,000
|
-10,000
|
|
Triplex
|
100,000
|
30,000
|
-12,000
|
|
Quadraplex
|
150,000
|
25,000
|
-20,000
|
a. Single unit
b. Duplex
c. Triplex
d. Quadraplex
Problem 13. What is the best decision based on the following table?
a. Single unit
b. Duplex
c. Triplex
d. Quadraplex
Problem 14. What is the critical path of this network?
|
Activity
|
Predecessor(s)
|
Duration
|
|
A
|
-
|
2
|
|
B
|
-
|
5
|
|
C
|
A
|
3
|
|
D
|
B
|
6
|
|
E
|
A,B
|
4
|
a. Start-A-E-End
b. Start-A-C-End
c. Start-B-D-End
d. Start-B-E-End
Problem 15. A probability distribution has been developed, and the probability of 2 arrivals in the next hour is 0.20. A random number interval is to be assigned to this. Which of the following would NOT be an appropriate interval?
a. 01-20
b. 21-40
c. 00-19
d. 00-20