Saint MBA550 full course (all homework + term project + all discussion +midterm +final exam)

Module 1

Chapter	Problems
1	2, 4
2	10, 12, 14

Chapter 1
Question2

The Retread Tire Company recaps tires. The fixed annual costof the recapping operation is $ 60,000. The variable cost ifrecapping tires is $9. The company charges $25 to recap atire.a) For an annual volume of 120,000 tires, determine the totalcost, total revenue, and profit.b) Determine the annual break-even volume for the Retread TireCompany operation.

Problem 4

Evergreen Fertilizer Company produces fertilizer. thecompany's fixed monthly cost is $25, 000 and its variable cost perpound of fertilizer is $0.15. Evergreen sells the fertilizer for$0.40 per pound. Determine the monthly break-even volume for thecompany.

Chapter 2

Problem 10
A large research hospital has accumulated statistical data on its patients for an extended period. Researchers have determined that patients who are smokers have an 18% chance of contracting a serious illness such as heart disease, cancer, of emphysema, whereas there is only a .06 probability that a nonsmoker will contract a serious illness. From hospital records, the researchers know that 23% of all hospital patients are smokers, while 77% are nonsmokers. For planning purposes, the hospital physician staff would like to know the probability that a gives patient is a smoker if the patient has a serious illness.

Problem 12
the senate consist of 100 senators, of whom 34 are republicans and 66 are democrats. A bil to increase appropriations is before the senate. thirty-five percent of the democrats and 70% of the republicans favor the bill. the bill needs a simple majority to pass. using a probability tree, determine the probability that the bill will pass.

Problem 14
A metropolitan school system consists of three districts – north, south, and central. The north district contains 25% of all students, the south district contains 40% of all students, and the central district contains 35%. A minimum competency test was given to all students. 10% of the north district students failed, 15% of the south district students failed, and 5% of the central district students failed.
A - develop a probability tree showing all marginal, conditional, and joint probabilities
B - develop a joint probability table.
C - What is the probability that a student selected at random failed the test

Module 2

Chapter	Problems
3	8, 26

problem 3-8

A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shown the profit or loss that could result from each investment.

Gasoline Availability

Investment Shortage Stable Supply Surplus

Motel $-8,000 $15,000 $20,000
Restuarant 2,000 8,000 6,000
Theater 6,000 6,000 5,000

Determine the best investment using the following decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz ( ? =.4)
e. Equal likelihood

problem 3-26

The Steak and Chop Butcher Shop purchases steak from a local meatpacking house. The meat is purchased on Monday at $2.00 per pound, and the shop sells the steak for $3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for $.50 per pound . The possible demands for steak and the probability of each are shown in the following table:
Demand (lb.) Probability
20 .10
21 .20
22 .30
23 .30
24 .10
1.00

The shop must decide how much steak to order in a week. Using Excel, construct a payoff table for this decision situation and determine the amount of steak that should be ordered, using expected value.

Module 3

Chapter	Problems
4	2, 38

2. The manger of the Carpet City outlet needs to make an accurate forecast of the demand of Soft Shag carpet (its biggest seller). If the manger does not order enough carpet from the carpet mill, customer will their carpet from one of Carpet City's many competitors. The manager has collected the following demand data for the past 8 months:

Demand for Soft Shag
Month Carpet (1,000 yd.)
1 8
2 12
3 7
4 9
5 15
6 11
7 10
8 12

a. Compute a 3- month moving average forecast for months 4 through 9.
b. Compute a weighed 3- month moving average forecast for months 4 through 9. Assign weights of .55, .33, and .12 to the months in sequence, starting with the most recent month.
c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?

6. The manager of the Petroco Service station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
Month Gasoline Demand (gal)
October 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1200
July 980

a. Compute and exponentially smoothed forecast, using on α value of .30.
b. Compute an adjusted exponentially smoothed forecast (with α =.30 and β=.20).
c. Compare the two forecast by using MAPD and indicate which seems to be more accurate.

Problem 4-38

Apperson and Fitz is a chain of clothing stores that caters to high school and college students. It publishes a quarterly catalog and operates a Web site that features provocatively attired males and females. The Web site is very expensive to maintain, and company executives are not sure whether the number of hits at the site relate to sales (i.e., people may be looking at the site's pictures only). The Web master has accumulated the following data for hits per month and orders placed at the Web site for the past 20 months:

Month Hits(1,000s) Orders(1,000s)
1 34.2 7.6
2 28.5 6.3
3 36.7 8.9
4 42.3 5.7
5 25.8 5.9
6 52.3 6.3
7 35.2 7.2
8 27.9 4.1
9 31.4 3.7
10 29.4 5.9
11 46.7 10.8
12 43.5 8.7
13 52.6 9.3
14 61.8 6.5
15 37.3 4.8
16 28.9 3.1
17 26.4 6.2
18 39.4 5.9
19 44.7 7.2
20 46.3 5.5

Develop a liner regression model for these data and indicate whether there appears to be a strong relationship between Web site hits and orders. What would be the forecast for orders with 50,000 hits per month?

Module 4

Chapter	Problems
5	8, 10, 12, 14
6	2, 4

Chapter 5 problem 8. The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturday. The ticket seller can serve an average of 12 customers per hour; on average, 10 customers arrive to purchase tickets each hour.

Determine the average time a ticket buyer must wait and the portion of time the ticket seller is busy.

10. The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 7.5 minutes, on average. The machine operator can process an average of 10 parts per hour. Determine the average number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the machine is idle.

12. The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway. Planes arrive at the airport at the rate of four per hour.

a. Determine the average number of planes that will stack up, waiting to land.
b. Find the average time a plane must wait in line before it can land.

14. During registration at State University every semester, students in the college of business must have their courses approved by the college adviser. It takes the adviser an average of 2 minutes to approve each schedule, and students arrive at the adviser's office at the rate of 28 per hour.

a. Compute L, Lq, W, Wq, and U.
b. The dean of the college has received a number of complaints from students about the length of time they must wait to have their schedules approved. The dean feels that waiting 10.00 minutes to get a schedule approved is not unreasonable. Each assistant the dean assigns to the advisor's office will reduce the average time required to approve a schedule by 0.25 minute, down to a minimum time of 1.00 minute to approve a schedule. How many assistants should the dean assign to the adviser?

Chapter 6

problem 2

Hayes Electronics assumes with certainty that the ordering cost is $450 per order and the inventory carrying cost is $170 per unit per year.However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty.Consider four cases of variation in the model parameters as follows:(a) both ordering cost and carrying cost are 10% lower than originally estimated.(b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated.

Determine the optimal order quantity and total inventory cost for each of the four cases.

Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values.

problem 4

The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 235,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $250 per order. It costs Western $1.65 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.

If possible, use Excel 3M or QM for Windows.

Module 5

Chapter	Problems
7	6, 13, 17

Module 6

Chapter	Problems
8	2, 6, 12
9	22, 24

For the module assignment, you must complete the problems below from your textbook:

For the Chapter 8 questions, answer part A only for each.

For 9-24, you must provide a solution for the problem that shows how you obtained your answers and specific answers to the questions.

2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

12. The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units and one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.

Module 7

.Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock.Betty stocks three brands of beer - Yodel, Shotz, and Rainwater.The cost per gallon (to the tavern owner) of each brand is as follows:

Brand Cost/gallon
Yodel $1.50
Shotz 0.90
Rainwater 0.50

The tavern has a budget of $2,000 for beer for Super Bowl Sunday.Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon.Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater.The tavern has a capacity to stock 1,000 gallons of beer; Betty wants to stock up completely.Betty wants to determine the number of gallons of each brand of beer to order so as to maximize profit.

a. Formulate a linear programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).
b. Solve this problem by using the computer.

3. Joe Henderson runs a small metal part shop. The shop contains three machines- a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three machines. However each operator performs better on some machines than on other. The shop has contracted to do a big job that requires all three machines. The times required by the various operators to perform the required operations on each machine are summarized as follows.

Operator Drill Press (min) Lathe (min) Grinder (min)
1 22 18 35
2 41 30 28
3 25 36 18

Joe Henderson wants to assign one operator to each machine so that the total operating time for all three operators in minimized.

A. Formulate a linear programming model for this problem
B. Solve the model using the computer
C. Joe's brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator. Kelly can perform each of the three required machine operations in 20 minutes. Should Joe hire his sister-in-law?

16. The athletic boosters club for Beaconville has planned a 2-day fund-raising drive to purchase uniforms for al the local high schools and to improve facilities. Donations will be solicited during the day and night by telephone and personal contact. The boosters club has arranged for local college students to donate their time to solicit donations. The average donation from each type of contact and the time for a volunteer to solicit each type of donations are as follows:
Average donation ($) Average Interview Time (min.)

Phone Personal Phone Personal
Day 16 33 6 13
Night 17 37 7 19
The boosters club has gotten several businesses and car dealers to donate gasoline and cars for the college students to use to make a maximum of 575 personal contacts daily during the fund-raising drive. The college students will donate a total of 22 hours during the day and 43 hours at night during the drive.
The president of the booster club wants to know how many different types of donor contacts to schedule during the drive to maximize the total donations. Formulate and solve an integer program between the integer and non-integer rounded-down solutions to this problem?

Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next 3 months. Each table will require 30 hours of labor, each chair will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of wood to make, and a chair requires 15 board feet. A table earns the couple $575 in profit. Most people who buy a table also want four chairs to go with it, so for every table that is produced, at least four chairs must also be made, although additional chairs can also be sold separately. Formulate and solve an integer programming model to determine the number of tables and chairs the Jacobsons should make to maximize profit.

MBA 550

Term Project Guidelines

Delicious Foods Corporation

The Delicious Foods Corporation makes nutrition (candy) bars. Next month (January) the company plans to sell nearly 200,000 pounds of candy (although they don't call it candy because they extol its nutritional value), which will be packaged as 600,000 bars; the price Delicious Foods will receive is 28 cents ($0.28) for each bar. Production capacity for the plant is 640,000 bars per month. The cost estimates for next month are:

Fixed Costs (do not vary with number of bars made)
Fixed manufacturing costs (factory overhead) $ 21,500
Fixed administrative costs (office overhead) 11,500
Advertising 4,500
Interest 4,100

Variable Costs (each of these is a "per bar" cost)
Labor 4 cents per bar
Materials 8 cents per bar

The planning horizon for Delicious Foods is the next five months, January thru
May. For January, the price will be $0.28 per bar; after that, the price will increase
to $0.29 for two months, and then to $0.30 for two months. The number of bars
made and sold is projected to begin at 600,000 bars, and then increase 2.5% each
month until the capacity of 640,000 bars is reached. Because of the rapid growth,
substantial increases in other costs are projected as follows:

Fixed manufacturing costs (factory overhead) increase 5% per month
Fixed administrative costs (office overhead) increase 7% per month
Advertising increase 8% per month
Interest will not change
Labor increase 10% per month
Materials increase 0.1 cents
($0.01) per bar each month

The General Manager (GM) is considering augmenting the advertising with a marketing cam¬paign designed to increase volume. This additional advertising would cost $7500 in January and $1500 in each of the remaining four months of the planning horizon. These campaign costs are in addition to the advertising costs already discussed. Once started, the marketing campaign must continue. The thrust of the campaign is to enhance the quantity of bars sold at the prices projected above. The GM believes that the campaign will either be a flop (leaving the quantity sold as projected), be moderately successful (bringing about an 8% monthly increase in quantity sold, instead of 2.5%), or be very successful (bring¬ing about a 15% monthly increase in quantity sold, instead of 2.5%). A decision to begin the campaign must be made within a day or two.
The campaign may not be a very good idea if the capacity limits (640,000 bars per month) are reached. Negotiations have taken place to obtain expanded facilities at the end of the first month, when it will be known if the advertising campaign is a flop, is moderately successful, or is very successful. The facilities expansion will cost $500 a month for the remaining four months, to increase capacity to 750,000 bars a month. Increasing the capacity to 1,000,000 bars a month would cost $1000 a month for the remaining four months. The capacity decision is made at the beginning of the second month; once made, it cannot be changed.
The probabilities of success for the campaign are flop, 0.1; moderate, 0.5; very successful, 0.4.

Analysis

What is the GM's primary issue at this point? The first decision that must be made is whether to undertake the advertising campaign. There is a secondary issue facing the GM: whether to expand the capacity of the factory. While it is known that there is enough capacity for January (planned production: 600,000 bars; capacity: 640,000 bars), it may be advantageous to obtain more capacity. If the campaign is started, the decision to obtain more capacity can be made after the first month's results are known. The GM believes that the growth rate in the first month will continue throughout the “planning horizon”. (Oh, how wordy that has become!) The purpose of the wordiness is to demonstrate vividly the ability of a decision tree to communicate the sequence of acts and events. Develop such a decision tree for the GM.
The scenario has provided the probability values, so they present no difficulty. The terminal values for profit will require substantial computation, however. A spreadsheet model is a useful way to calculate these terminal values. The model should calculate the profit before tax for any combination of campaign decision, campaign event (bar growth rate), and capacity decision. Rather than attempt to develop one model to simultaneously evaluate all end points, you should try to build one model that can be used to evaluate each end point by changing the values in a few cells.

Activities:

Write a report for the GM (and be prepared to present it).
a. Construct a spreadsheet model using the data provided.
b. Use the model to find all terminal values in the decision tree.
c. Construct the decision tree, placing probabilities on appropriate branches.
d. Use the tree to recommend a course of action.
e. What would be the end result (net income) if the worst possible set of events occurred? Discuss.
f. What would be the end result (net income) if the best possible set of events occurred? Discuss.

g.Which would be worse, to have a very successful ad campaign and not expand production or to have a poor ad campaign and expand production? (Assume you don’t know the result of the campaign before you have to decide on expansion.) Why. Explain in detail.
h.At what cost for expanded capacity would expansion become infeasible? Explain.