I hope this goes better than last time,” thought Craig Rooney as he thought about having to walk into the city council’s chambers next week. Craig is the assistant chief of police in Newport, VA and, each September, he has to provide the city council with a report on the effectiveness of the city’s police force. This report immediately precedes the council’s discussion of the police department’s budget. So Craig often feels like a tightrope artist trying to find the right balance in his presentation to both convince the council that the department is being run well and also persuade them to increase the department’s budget for new officers. The city of Newport has a total of 19 police officers assigned to 5 precincts. Currently, precinct A has 3 officers assigned to it while the others each have 4 officers. One of the town council’s primary concerns each year is the amount of time it takes for an officer to begin responding when a 911 emergency call is received. Unfortunately, the city’s information system does not track this data exactly, but it does keep track of the number of calls received in each precinct each hour and the amount of time that elapses between when an officer first begins responding to a call and the time he or she reports being available again to respond to other calls (this is also known as the service time for each call). A student intern from a local university worked for Craig last summer and collected data shown in the file named CallData.xlsm that accompanies this book. One of the sheets in this workbook (named calls per hour) shows the number of 911 calls received during 500 randomly chosen hours of operation in each precinct. Another sheet (named service times) shows the service times required for each of these calls. The student intern also set up a worksheet (based on the formulas in Figure 13.6) to calculate operating characteristics of an M/M/s queue for each of the Newport’s 5 precincts. Unfortunately, the student interim had to return to school before finishing this project. But Craig believes with a little work he can use the data collected to figure out appropriate arrival and service rates for each precinct and complete the analysis. More importantly, he feels sure the queuing model will allow him to quickly answer many of the questions he expects the city council to ask. a. What are the arrival rate of 911 calls and the service rates for each precinct? b. Does the arrival rate of calls for each precinct appear to follow a Poisson distribution? c. Does the service rate for each precinct appear to follow an exponential distribution? d. Using an M/M/s queue, on average, how many minutes must a 911 caller in each precinct wait before a police officer begins responding? e. Suppose Craig wants to redistribute officers among precincts so as to reduce the maximum amount of time callers in any one precinct have to wait for a police response. What should he do and what impact would this have? f. How many additional police officers would Newport have to hire in order for the average response time in each precinct to be less than 2 minutes?
> A paper recycling company converts newspaper, mixed paper, white office paper, and cardboard into pulp for newsprint, packaging paper, and print stock quality paper. The following table summarizes the yield for each kind of pulp recovered from each ton o
> The Sentry Lock Corporation manufactures a popular commercial security lock at plants in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is $35.50, $37.50, $39.00, and $36.25, respectively, while the annual producti
> The Pelletier Corporation has just discovered that it will not have enough warehouse space for the next five months. The additional warehouse space requirements for this period are listed in the following table: To cover its space requirements, the firm
> The Pitts Barbecue Company makes three kinds of barbecue sauce: Extra Hot, Hot, and Mild. Pitts’ vice president of marketing estimates that the company can sell 8,000 cases of its Extra Hot sauce plus 10 extra cases for every dollar it spends promoting t
> Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residences in the Blacksburg area. The plant burns three types of coal, which produce steam that
> Sam Ellis is worried. As president and CEO of Forward Software, Sam introduced a new spreadsheet product, Cinco, to the market last year. Forward Software has been developing and marketing high-quality software packages for more than 5 years, but these p
> Radmore Memorial Hospital has a problem in its fluids analysis lab. The lab has three machines available that analyze various fluid samples. Recently, the demand for analyzing blood samples has increased so much that the lab director is having difficult
> Holiday Fruit Company buys oranges and processes them into gift fruit baskets and fresh juice. The company grades the fruit it buys on a scale from 1 (lowest quality) to 5 (highest quality). The following table summarizes Holiday’s curr
> A manufacturer of prefabricated homes has decided to subcontract four components of the homes. Several companies are interested in receiving this business, but none can handle more than one subcontract. The bids made by the companies for the various subc
> The Shop at Home Network sells various household goods during live television broadcasts. The company owns several warehouses to hold many of the goods it sells but also leases extra warehouse space when needed. During the next five months the company ex
> A company is trying to determine how to allocate its $145,000 advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for advertising. The following table summarizes the costs of adve
> The Molokai Nut Company (MNC) makes four different products from macadamia nuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts
> Riverside Oil Company in eastern Kentucky produces regular and supreme gasoline. Each barrel of regular sells for $21 and must have an octane rating of at least 90. Each barrel of supreme sells for $25 and must have an octane rating of at least 97. Each
> A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual return. The officer wants to invest at least 50% of the money in short-term issues and no more than 50
> Valu-Com Electronics manufactures five different models of telecommunications interface Cards for PCs and laptops. As summarized in the following table, each of these devices requires differing amounts of printed circuit board, resistors, memory chips, a
> Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs ar
> In the mid-1990s, DHL was the world’s largest shipping company, with $5.7 billion in revenue and 60,000 employees. Larry Hillbloom was the “H” in DHL and founder of the company. DHL started on a shoestring budget in 1969 with a business plan to deliver s
> Create a Sensitivity Report for Electro-Poly’s make vs. buy problem in section 3-9 of Chapter 3 and answer the following questions. a. Is the solution degenerate? b. How much can the cost of making model 1 slip rings increase before it becomes more econo
> Use Solver to create Answer and Sensitivity Reports for question 26 at the end of Chapter 2 and answer the following questions: a. If the profit on doors increased to $700 would the optimal solution change? b. If the profit on windows decreased to $200 w
> The Rent-A-Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its locations. Currently, two locations (1 and 2) have 16 and 18 surplus cars, respectively, and four locations (3, 4, 5, and 6) each
> The Weed wacker Company manufactures two types of lawn trimmers: an electric model and a gas model. The company has contracted to supply a national discount retail chain with a total of 30,000 electric trimmers and 15,000 gas trimmers. However, Weed mwac
> Bear land Manufacturing produces 4 different types of wood paneling. Each type of paneling is made by gluing and pressing together a different mixture of pine and oak chips. The following table summarizes the required amount of gluing, pressing, and mix
> Krouscas Foods makes a special blend of oil that is popular in Greek cooking. They import oil from two vendors and blend it to ensure that the resulting product contains at least 40% olive oil, 20% sunflower oil, and at least 30% corn oil. Vendor 1 can p
> Game Day Fashions makes custom t-shirts for fans of college university sports teams. Currently, the company is trying to determine the best way to fill an order it received from Sable University. The official colors of Sable University are orange and ma
> This chapter introduces the quote “All models are wrong, but some are useful.” from George Box. Describe a real-world situation where a model was wrong but useful.
> Refer to question 27 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver. Data from question 27 chapter 2: PC-Express is a computer retail store that sells desktops and laptops. The company earns $600 on e
> Refer to question 26 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver Data from question 26 chapter 2: Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produce
> In a summer plagued by drought and heat, many Southern crops are withering in the fields, taking farmers’ profits down with them. Some farmers are fighting to break even. But others have had to give up hope that this year’s crop will survive to harvest.
> Refer to question 25 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver. Data from question 25 chapter 2: A farmer in Georgia has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre
> Refer to question 24 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver. Data from question 24 chapter 2: The Quality Desk Company makes two types of computer desks from laminated particle board. The Pre
> Refer to question 23 at the end of Chapter 2. Implement a spreadsheet model for this problem and solve it using Solver Data from question 23 chapter 2: Zippy motorcycle manufacturing produces two popular pocket bikes (miniature motorcycles with 49cc en
> The following data summarizes the per-day cost of crashing the activities in the problem described in the previous question. a. Create an LP model to determine the least costly way of crashing the project to complete it within 20 days. b. By how much sh
> Consider the following set of activities: a. Draw the CPM network for this problem. b. Create a spreadsheet to calculate and summarize the earliest and latest start and finish times, the slack for each activity, and the critical activities. c. What is t
> Consider the following set of activities: a. Draw the CPM network for this problem. b. Identify each path through the network and its expected length. c. What is the critical path?
> Consider the following set of activities: a. Draw the CPM network for this problem. (Remember that a CPM network requires unique start and finish nodes.) b. Manually determine the earliest and latest start and finish times for each activity and the amou
> Consider the following set of activities: a. Draw the CPM network for this problem. b. Manually determine the earliest and latest start and finish times for each activity and the amount of slack for each activity. c. What is the critical path? d. How lo
> Consider the CPM network for the following set of activities: Is it necessary to draw an arc from the node for activity A to the node for activity C? Why or why not?
> In illustrating how to simulate an activity network, we used a triangular distribution based on three time estimates to generate random activity times. What problem might be encountered if we assume that activity times were normally distributed? (Hint: C
> Anyone who has suffered with an acute or chronic illness is probably very appreciative for whatever drugs are available to cure or manage the disease. In the United States, the Food and Drug Administration (FDA) is the governmental agency that oversees t
> Refer to the previous problem. Suppose that the maximum time listed for each activity is actually its normal completion time. Further assume that the maximum number of crash days per activity and cost per crash day are as follows: a. Create and solve an
> A cosmetics company has identified a set of activities that must be performed in order to bring a new product to market. The activities, their precedence relations, and time estimates to complete each activity (in days) are shown in the following table.
> The activities summarized in the following table must be performed by the promoter of a country music concert in Dallas. a. Draw the activity network for this problem. b. According to PERT, what is the expected length of time required to accomplish thes
> Refer to the previous question. Create a spreadsheet model to simulate the completion times for the auditing project. Assume that activity times follow a triangular distribution and perform 500 replications on the model. a. Estimate the probability of ea
> A partner in the national accounting firm mentioned in the previous questions does not believe the time estimates for each activity can be specified with certainty. Instead, she prefers to specify a minimum, most likely, and maximum time estimate for eac
> Refer to the previous question. Suppose that each of the audit activities can be crashed by the amounts indicated in the following table. a. What is the earliest the audit could be completed and what is the incremental cost associated with this schedule
> A national accounting firm has identified the following set of activities that must occur to carry out an audit for one of their major clients a. Draw the CPM network for this problem. b. Create a spreadsheet to calculate and summarize the earliest and
> Throughout this chapter, we assumed that a project manager identifies and organizes the activities in a project, estimates the time required for each activity, then determines how quickly the project can be completed. However, the deadlines for some proj
> Refer to the previous question. Create a spreadsheet model to simulate the completion times for Koene’s move. Assume that activity times follow a triangular distribution and perform 500 replications on the model. a. Estimate the probab
> Refer to the previous question. Suppose a partner in Koene Technology does not believe the time estimates for each activity can be specified with certainty. Instead, he prefers to specify a minimum, most likely, and maximum number of days for each activi
> Koene Technology is a rapidly growing nanotechnology firm. The company is moving into a new building that will allow it more research lab space and improved computing facilities. The lease on the new facility has already been signed and architectural ren
> Refer to the previous question. Create a spreadsheet model to simulate the completion times for servicing cars. Assume that activity times follow a triangular distribution, and perform 500 replications on the model. a. Estimate the probability of each ac
> The activities required to service a car at Zippy-Lube can be viewed as a mini-project as summarized in the following table. The variability in the time required to perform each activity is due to the different types, sizes, and condition of the cars to
> Refer to the previous question. Suppose that Linda’s lease on her current facility expires in 20 days. The normal and crash times and costs for each activity in her moving project are summarized in the following table. By what amount sh
> Linda Madison owns Creations, a business that provides hair and nail care services in a small college town. Recently, Linda has decided to expand her business to include tanning and massage services for her clients. In order to accommodate these new serv
> A software company is moving its helpdesk operations center from Newark, New Jersey to Plano, Texas. Some of its employees will be moved to Plano and others will be terminated and replaced by new workers in Texas. The activities that must be carried out
> Aerobatic, Inc. custom designs and manufactures light aircraft. The activities involved in this process are summarized in the following table. a. Draw the activity network for this problem. b. Create a spreadsheet to calculate and summarize the earliest
> The Runabout Boat Company is considering the purchase of several units of an expensive new machine for its production facilities around the country. Before committing to this purchase, Runabout wants to set up a test facility to test the machine and make
> In this chapter, we stated that the longest path through an activity network is the critical path. Why isn’t the completion time for a project defined by the shortest path through the network? Explain your answer.
> Morley Properties is planning to build a condominium development on St. Simons Island, Georgia. The company is trying to decide between building a small, medium, or large development. The payoffs received for each size of development will depend on the m
> The Foxridge Investment Group buys and sells rental income properties in Southwest Virginia. Bill Hunter, president of Foxridge, has asked for your assistance in analyzing a small apartment building the group is interested in purchasing.The property in q
> Bob Farrell, owner of Farrell Motors, is trying to decide whether to buy an insurance policy to cover hail damage on his inventory of more than 200 cars and trucks. Thunderstorms occur frequently and they sometimes produce hail the size of golf balls tha
> A car dealer is offering the following three 2-year leasing options: Assume a customer expects to drive between 15,000 and 35,000 miles during the next 2 years according to the following probability distribution: a. Construct a payoff matrix for this p
> The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the d
> Lori Henderson runs a specialty ski clothing shop outside of Boone, North Carolina. She must place her order for ski parkas well in advance of ski season because the manufacturer produces them in the summer months. Lori needs to determine whether to plac
> One of Philip Mahn’s investments is going to mature, and he wants to determine how to invest the proceeds of $30,000. Philip is considering two new investments: a stock mutualfund and a one-year certificate of deposit (CD). The CD is guaranteed to pay an
> Identify a consumer electronics product that you want to purchase (e.g., a TV, digital camera, tablet computer, and so on). Identify at least three models of this product that you would consider purchasing. Identify at least three criteria on which these
> Kathy Jones is planning to buy a new minivan but, after narrowing her choices down to three models (X, Y, and Z) within her price range, she is having difficulty deciding which one to buy. Kathy has compared each model against the others on the basis of
> The president of Pegasus Corporation is trying to decide which of the three candidates (denoted as candidates A, B, and C) to hire as the firm’s new vice president of marketing. The primary criteria the president is considering are each
> Hiro Tanaka is going to purchase a new car and has narrowed the decision down to three different sedans. The following table summarizes how he rates each sedan on the criteria that are most important to him. Upon reflection, Hiro decides that the weight
> Consider the following payoff matrix: Should a decision maker ever select decision alternative C? Explain your answer.
> Marissa Jones is the president and CEO of Sound’s Alive, a company that manufactures and sells a line of speakers, CD players, receivers, high-definition televisions, and other items geared for the home entertainment market. Respected throughout the indu
> Rusty Reiker is looking for a location to build a new restaurant. He has narrowed the options down to three possible locations. The following table summarizes how he rates each location on the criteria that are most important to his business. Upon refle
> Suppose that you are given the following two alternatives: a. At what value of p would you be indifferent between these two alternatives? b. Given your response to part (a), would you be classified as risk averse, risk neutral, or risk seeking? c. Suppo
> Thom DeBusk, an architect, is considering buying, restoring, and reselling a home in the Draper-Preston historic district of Blacksburg, VA. The cost of the home is $240,000 and Thom believes it can be sold for $450,000 after being restored. Thom expects
> Eagle Credit Union (ECU) has experienced a 10% default rate with its commercial loan customers (i.e., 90% of commercial loan customers pay back their loans). ECU has developed a statistical test to assist in predicting which commercial loan customers wil
> Johnstone & Johnstone (J&J) has developed a new type of hand lotion with a distinctive fragrance. Before distributing it nationally, J&J will test market the new product. The joint probability of a successful test market and high sales upon national dist
> The Mobile Oil company has recently acquired oil rights to a new potential source of natural oil in Alaska. The current market value of these rights is $90,000. If there is natural oil at the site, it is estimated to be worth $800,000; however, the compa
> From industry statistics, a credit card company knows that 0.8 of its potential cardholders are good credit risks and 0.2 are bad credit risks. The company uses discriminate analysis to screen credit card applicants and determine which ones should receiv
> Refer to the previous question. The present value (PV) of a future cash-flow value (FV) is defined as: where n is the number of years into the future in which the cash flow occurs and r is the discount rate. Suppose that the discount rate for Banisco is
> The Banis co Corporation is negotiating a contract to borrow $300,000 to be repaid in a lump sum at the end of 9 years. Interest payments will be made on the loan at the end of each year. The company is considering the following three financing arrangeme
> Bulloch County has never allowed liquor to be sold in restaurants. However, in 3 months, county residents are scheduled to vote on a referendum to allow liquor to be sold by the drink. Currently, polls indicate there is a 60% chance that the referendum w
> Throughout our discussion of regression analysis, we used the Regression command to obtain the parameter estimates that minimize the sum of squared estimation errors. Suppose that we want to obtain parameter estimates that minimize the sum of the absolut
> US Express is an overnight package delivery company based in Atlanta, Georgia. Jet fuel is one of the largest operating costs incurred by the company, and the company wants your assistance in managing this cost. The price of jet fuel varies considerably
> Give an example of a national business, political, or military leader who made a good decision that resulted in a bad outcome, or a bad decision that resulted in a good outcome.
> Southern Gas Company (SGC) is preparing to make a bid for oil and gas leasing right in a newly opened drilling area in the Gulf of Mexico. SGC is trying to decide whether to placea high bid of $16 million or a low bid of $7 million. SGC expects to be bid
> Refer to the previous question. A manufacturing engineer for MPI collected the following data on the failure rates of components X, Y, and Z in a random sample of 1,000 circuit boards: For example, the first row in this table indicates that components X
> Microproducts, Incorporated (MPI) manufactures printed circuit boards for a major PC manufacturer. Before a board is sent to the customer, three key components must be tested. These components can be tested in any order. If any of the components fail, th
> Bill and Ted are going to the beach with hopes of having an excellent adventure. Before going, they read a report by the world’s leading authority on tiger shark behavior indicating that when a tiger shark is in the vicinity of swimmers at the beach, the
> A manufacturer has two machines that make the same parts for diesel truck engines. One machine is 5 years older than the other one. The older machine runs slower and makes 35% of the parts, of which 85% are of acceptable quality and don’t require rework.
> Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will indicate the presence of heart disease. When a person without heart disease is giv
> The Tall Oaks Wood Products Company is considering purchasing timberland for $5 million that would provide a future source of timber supply for the company’s operations over the next 10 years. Alternatively, for $5 million, the company could also buy tim
> Refer to question 10. Suppose that the consultant’s fee is $5,000 and the utility function for the owner of Morley Properties can be approximated by the exponential utility function: where the risk tolerance value R 5 100 (in $1,000s)
> Refer to question 9. Suppose that the utility function for the owner of Morley Properties can be approximated by the exponential utility function: where the risk tolerance value R 5 100 (in $1,000s). a. Convert the payoff matrix to utility values. b. W
> Benjamin Franklin once said, “In this world nothing is certain but death and taxes.” Although that may be true, there is often great uncertainty involved in when one will encounter death and how much one must pay in ta
> Refer to the previous question. Morley Properties can hire a consultant to predict the most likely level of demand for this project. This consultant has done many similar studies and has provided Morley Properties with the following joint probability tab
> This chapter presented the problem of having to decide between two job offers. The decision maker could accept the job with company A, accept the job with company B, or reject both offers and hope for a better one. What other alternatives can you think o
> Refer to questions 6 and 7 and answer the following questions: a. What is the probability that the drive-in window is empty? b. What is the probability that a customer must wait for service? c. On average, how many cars wait for service? d. On average, w
> Suppose that arrivals to a queuing system with one server follow a Poisson distribution with an average of l 5 5 per time period, and that service times follow an exponential distribution with an average service rate of m 5 6 per time period. a. Compute
> Refer to the previous question. Suppose that Road Rambler’s phone system can only keep 4 calls on hold at any time, the average profit margin of each call is $55, and sales reps cost the company $12 per hour. a. If callers who receive a busy signal tak
> Calls to the service center at AutoMax occur at a rate of 27 per hour and follow a Poisson distribution. A single operator answers the calls and can handle an average 25 calls per hour with service times following an exponential distribution. If a call a
