Homework:
Homework group (2-3 students) must be submitted by the end of each chapter
Chapter 2 (Introduction to Probability and Probability Distributions)
Some homework will be given in the class.
Q1 A class contains 30 students. 10 are female (F) and US citizens (U); 12 are male (M) and US citizens; 6 are female and non-US citizens (N); 2 are male and non-US citizens.
1. A name is randomly selected from the class what is the probability of getting female?
2. A name is randomly selected from the class what is the probability of getting female and US citizen?
3. A name is randomly selected from the class and it is female, what is the probability that the student is a US citizen?
Q2A candidate for public office has claimed that 60% of voters will vote for her. If 5 registered voters were sampled,
1. What is the probability distribution for this voting?
2. What is the probability that exactly 3 would say they favor this candidate?
3. Calculate the mean and standard deviation of the probability distribution
Q3 the length of the rods coming out of our new cutting machine can be said to approximate a normal distribution with a mean of 10 inches and a standard deviation of 0.2 inch. Find the probability that a rod selected randomly will have a length
1. Of less than 10 inches
2. Between 10 and 10.4 inches
3. Between 10 and 10.1 inches
4. Between 9.6 and 9.9 inches
5. Between 9.9 and 10.4 inches
Q4 A coin is flipped twice. Calculate the probability of each of the following occurring:
1. A head on the first flip
2. A tail on the second flip given that the first toss was a head
3. Two tails
Q5 A student taking Management science at East Haven University will receive one of the five possible grades for the course: A, B, C, D, E, or F. The distribution of grades over the past two years is as follows:
Grade Number of students
A 80
B 75
C 90
D 30
F 25
If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course?
Chapter 3 (Forecasting)
.0/msohtmlclip1/01/clip_image002.jpg” alt=”http://questions.transtutors.com/Transtutors001/Images/Transtutors001_ec047852-934a-4191-879a-113ca6821238.png”>Q1 Emergency calls to Winter Park, Floridas 911 systems for the past 24 weeks are as follows:
(a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 50 calls in the first week and use alpha = 0.1. What is the forecast for the 25th week?
(b) Reforecast each period using alpha = 0.6.
(c) Actual calls during the 25th week were 85. Which smoothing constant provides a superior forecast?
Q2 Sales of Cool-Man air conditioners have grown steadily over the past five years:
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a. The sales manager had predicted, before the business started, that year 1s sales would be 410 units. Using exponential smoothing with a weight of ? = 0.30, develop forecasts for years 2 through 6.
b. Using the smoothing coefficients of 0.60 and 0.90, develop forecasts for the sales of Cool- Man air conditioners.
c. What effect did the smoothing coefficient have on the forecast for Cool-Man air conditioners? Which smoothing coefficient gives the most accurate forecast?
Chapter 4 (Linear Programming Models: Graphical and Computer Methods)
Q1 A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in thedays preceding the election. Two types of ads will be used: radio and television. Eachradio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many peopleas possible, but she has stipulated that at least 10ads of each type mustbe used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?
Q2 The Outdoor Furniture Corporation manufacturing two products, benches and picnic tables,foruse in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit?
Q3 The dean of the Western College of Business must plan the schools course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?
Q4 MSA Computer Corporation manufactures two models of minicomputers, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next months operations. It requires 20 labor hours to assemble each Alpha 4computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of minicomputer to produce during the coming month.
Chapter 5 (Transportation and Assignment Models)
Q1 The Krampf Lines Railway Company specializes in coal handling. On Friday, April 13, Krampf had empty cars at the following towns in the quantities indicated:
TOWN
SUPPLY OF CARS
Morgantown
35
Youngstown
60
Pittsburgh
25
By Monday, April 16, the following towns will need coal cars as follows:
TOWN
DEMAND FOR CARS
Coal Valley
30
Coaltown
45
Coal Junction
25
Coalsburg
20
Using a railway city-to-city distance chart, the dispatcher constructs a mileage table for the preceding towns. The result is shown in the table below. Minimizing total miles over which cars are moved to new locations, compute the best shipment of coal cars.
TO
COAL VALLEY
COALTOWN
COAL JUNCTION
COALSBURG
FROM
MORGANTOWN
50
30
60
70
YOUNGSTOWN
20
80
10
90
PITTSBURGH
100
40
80
30
Q2 The three blood banks in Franklin County are coordinated through a central office that facilitates blood delivery to four hospitals in the region. The cost to ship a standard container of blood from each bank to each hospital is shown in the table below. Also given are the biweekly number of containers available at each bank and the biweekly number of containers of blood needed at each hospital. How many shipments should be made biweekly from each blood bank to each hospital so that total shipment costs are minimized?
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Chapter 6 (Network Models)
Q1 Bechtold Construction is in the process of installing power lines to a large housing development. Steve Bechtold wants to minimize the total length of wire used, which will minimize his costs. The housing development is shown as a network in the Figure below. Each house has been numbered, and the distances between houses are given in hundreds of feet. What do you recommend?
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Q2 Because of a sluggish economy, Bechtold Construction has been forced to modify its plans for the housing development in previous problem. The result is that the path from node 6 to 7 now has a distance of 7.What impact does this have on the total length of wire needed to install the power lines?
Q3 Solve the minimal-spanning tree problem in the network shown in Figure 11.26. Assume that the numbers in the network represent distance in hundreds of yards.
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Q4 Refer to the previous problem. What impact would changing the value for path 6-7 to 500 yards have on the solution to the problem and the total distance?
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Chapter 7 (Project Management)
.0/msohtmlclip1/01/clip_image015.gif”>Q1 The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are independent.
Calculate the expected time and variance for each activity.
(b) What is the expected completion time of the critical path? What is the expected completion time of the other patient in the network?
(c) What is the variance of the critical path? What is the variance of the other path in the network?
(d) If the time to complete path A-C is normally distributed, what is the probability that this path will be finished in 22 weeks or less?
(e) If the time to complete path B-D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?
Q2to complete the wing assembly for an experimental aircraft, Scott DeWitte has laid out the major steps and seven activities involved. These activities have been labeled A through G in the following table, which also shows their estimated completion times (in weeks) and immediate predecessors.
Draw the network associated with the above activities
Determine the expected time and variance for each activity.
Determine the critical path for the entire wing assembly project as well as the expected completion timefor the total project.
What is the probability that the project will be completed in 18 weeks?
activity
a
m
b
?mmediate predessors
A
1
2
3
–
B
2
3
4
–
C
4
5
6
A
D
8
9
10
B
E
2
5
8
C, D
F
4
5
6
B
G
1
2
3
E
Q3Tom Schriber, a director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the information on the activities is showing in the following table:
activity
days
?mmediate predecessors
a
m
b
A
8
10
12
–
B
6
7
9
–
C
3
3
4
–
D
10
20
30
A
E
6
7
8
C
F
9
10
11
B,D,E
G
6
7
10
B,D,E
H
14
15
16
F
I
10
11
13
F
J
6
7
8
G,H
K
4
7
8
I,J
L
1
2
4
G,H
Construct a network for this problem
Determine the expected time and variance for each activity
Determine ES, EF, LS, LF, and slack for each activity
Determine the critical path and project completion time
Determine the probability that the project will be finished in 70 days or less
Determine the probability that the project will be finished in 80 days or less
Determine the probability that the project will be finished in 90 days or less