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essential statistics
Statistics Data Analysis And Decision Modeling 5th International Edition James R. Evans - Solutions
14. The Spurling Group is considering using magazine outlets to advertise their online Web site. The company has identified seven publishers. Each publisher breaks down their subscriber base into a number of groups based on demographics and location. These data are shown in the table
13. Mark Haynes is interested in buying a new car. He decided on a particular model, which has lots of options from which to choose. The base price of the car is $16,510 and he allotted a budget of $19,250 to purchase it. The table below shows the possible options over and above the base model that
12. Chris Corry has a company-sponsored retirement plan at a major brokerage firm. He has the following funds available:Fund Risk Type Return 1 High Stock 11.98%2 High Stock 13.18%3 High Stock 9.40%4 High Stock 7.71%5 High Stock 8.35%6 High Stock 16.38%7 Medium Blend 4.10%8 Medium Blend 12.52%9
11. Josh Steele manages a professional choir in a major city.His marketing plan is focused on generating additional local demand for concerts and increasing ticket revenue, and also gaining attention at the national level to build awareness of the ensemble across the country.He has $20,000 to spend
10. Brewer Services contracts with outsourcing partners to handle various customer service functions. The customer service department is open Monday through Friday from 8 a.m. to 5 p.m. Calls vary over the course of a typical day. Based on a study of call volumes provided by one of the firm’s
9. Anya is a part-time MBA student who works fulltime and is constantly on the run. She recognized the challenge of eating a balanced diet and wants to minimize cost while meeting some basic nutritional requirements. Based on some research, she found that a very active woman should consume 2,250
8. Dannenfelser Design works with clients in three major project categories: architecture, interior design, and combined. Each type of project requires an estimated number of hours for different categories of employees as shown in the table below.Architecture Interior Design Combined Hourly Rate
7. Premier Paints supplies to major contractors. One of their contracts for a specialty paint requires them to supply 750, 500, 400, and 950 gallons over the next 4 months. To produce this paint requires a shutdown and cleaning of one of their manufacturing departments at a cost of $1,000. The
6. Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a threehour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible
4. A medical device company is allocating next year’s budget among its divisions. As a result, the R&D Division needs to determine which research and development projects to fund. Each project requires various software and hardware and consulting expenses, along with internal human resources. A
3. The personnel director of a company that recently absorbed another firm and is now downsizing and must relocate five information systems analysts from recently closed locations. Unfortunately, there are only three positions available for five people. Salaries are fairly uniform among this group
2. For the cutting stock example in the chapter, suppose that the scrap generated from each pattern costs $2 per inch. The company also incurs a fixed cost for setting up the machine to cut different patterns. These costs are:Pattern Fixed Cost 1 $70 2 $40 3 $40 4 $90 5 $50 6 $80 Modify the model
1. Thermal transfer printing transfers ink from a ribbon onto paper through a combination of heat and pressure.Different types of printers use different sizes of ribbons.A ribbon manufacturer has forecasted demands for seven different ribbon sizes:Size Forecast (Rolls)60 mm 1,620 83 mm 520 102 mm
8. How can Crystal Ball and OptQuest enhance the analysis of optimization problems?
7. What are metaheuristics ? What are the tools in Excel that can implement such approaches?
6. What is a local optimum solution? What should you do to improve your chances of getting a global optimum solution?
5. In both the plant location and fixed-cost models presented in this chapter, we used “linking” constraints that established a relationship between the binary variables and other continuous variables in the model.Why are such constraints necessary in any mixed integer model?
4. How can binary variables be used to model logical conditions?Provide several examples.
3. Why can’t Sensitivity Reports be produced for integer models in Solver in the usual manner?
2. What is a mixed linear optimization model?
1. What is an integer program?
25. Jason Wright is a part-time MBA student who would like to optimize his financial decisions. Currently, he has $16,000 in his savings account. Based on an analysis of his take-home pay, expected bonuses, and anticipated tax refund, he has estimated his income for each month over the next year.
24. An international graduate student will receive a $28,000 foundation scholarship and reduced tuition. He must pay $1,500 in tuition for each of the autumn, winter, and spring quarters, and $500 in the summer. Payments are due on the first day of September, December, March, and May, respectively.
23. Raturi and Rao, Inc. produces four industrial chemicals with variable production costs of $9.00, $6.75,$5.25, and $7.50 per pound, respectively. Because of increasing supplier costs, the variable cost of each of the products will increase by 6% at the beginning of month three. Demand forecasts
22. Mirza Manufacturing makes four electronic products, each of which is comprised of three main materials:magnet, wiring, and casing. The products are shipped to three distribution centers in North America, Europe, and Asia. Marketing has specified that no location should receive more than the
21. Shafer Office Supplies has four distribution centers located in Atlanta, Cincinnati, Chicago, and Salt Lake City, and ships to 12 retail stores located in Portland, San Jose, Las Vegas, Tucson, Colorado Springs, Kansas City, St. Paul, Austin, Jackson, Montgomery, Cleveland, and Pittsburgh. The
20. The Kelly Company is a producer of canned vegetables.The company’s food processing plants are located in Sacramento and Dallas. Distribution centers are located in Denver, Cincinnati, Phoenix, and Atlanta. The supply chain manager wants to minimize the cost of shipping the goods from the
19. The Children’s Theater Company is a nonprofit corporation managed by Shannon Board. The theater performs in two venues: Kristin Marie Hall and the Lauren Elizabeth Theater. For the upcoming season, seven shows have been chosen. The question Shannon faces is how many performances of each of
18. Liquid Gold, Inc. transports radioactive waste from nuclear power plants to disposal sites around and about the country. Each plant has an amount of material that must be moved each period. Each site has a limited capacity per period. The cost of transporting between sites is given here (some
17. The Hansel Corporation, located in Bangalore, India, makes plastics materials that are mixed with various additives and reinforcing materials before being melted, extruded, and cut into small pellets for sale to other manufacturers. Four grades of plastic are made, each of which might include
16. Young Energy operates a power plant that includes a coal-fired boiler to produce steam to drive a generator.The company can purchase different types of coals and blend them to meet the requirements for burning in the boiler. The table below shows the characteristics of the different types of
15. The International Chef, Inc. markets three blends of oriental tea: premium, Duke Grey, and breakfast. The firm uses tea leaves from India, China, and new domestic California sources.Tea Leaves (%)Quality Indian Chinese California Premium 40 20 40 Duke Grey 30 50 20 Breakfast 40 40 20 Net profit
14. Janette Douglas is coordinating a bake sale for a nonprofit organization. The organization has acquired$2,200 in donations to hold the sale. The table below shows the amounts and costs of ingredients used per batch of each baked good:Ingredient Brownies Cupcakes Peanut Butter Cups Shortbread
13. Sandford Tile Company makes ceramic and porcelain tile for residential and commercial use. They produce three different grades of tile (for walls, residential flooring, and commercial flooring), each of which requires different amounts of materials and production time, and generates different
12. Roberto’s Honey Farm in Chile makes five types of honey: cream, filtered, pasteurized, mélange (a mixture of several types), and strained, which are sold in 1 or 0.5 kg glass containers, 1 kg and 0.75 kg plastic containers, or in bulk. Key data are shown in the following table.Selling Prices
11. Jaycee’s department store chain is planning to open a new store. It needs to decide how to allocate the 100,000 square feet of available floor space among seven departments. Data on expected performance of each department per month, in terms of square feet (sf), are shown below.Department
10. Holcomb Candles, Inc. manufactures decorative candles and has contracted with a national retailer to supply a set of special holiday candles to its 8,500 stores. These include large jars, small jars, large pillars, small pillars, and a package of four votive candles. In negotiating the contract
9. A recent MBA graduate, Dara, has gained control over custodial accounts that her parents had established.Currently, her money is invested in four funds but she has identified several other funds as options for investment.She has $100,000 to invest with the following restrictions:• Keep at
8. Beverly Ann Cosmetics has created two new perfumes:Summer Passion and Ocean Breeze. It costs$5.25 to purchase the fragrance needed for each bottle of Summer Passion, and $4.70 for each bottle of Ocean Breeze. The marketing department has stated that at least 30% but no more than 70% of the
7. Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively.The projected monthly sales are:Small Medium Large Minimum 14,000 6,200 2,600 Maximum 21,000 12,500 4,200 The production process
6. Marketing managers have various media alternatives, such as radio, TV, magazines, etc., in which to advertise and must determine which to use, the number of insertions in each, and the timing of insertions to maximize advertising effectiveness within a limited budget. Suppose that three media
5. Rosenberg Land Development (RLD) is a developer of condominium properties in the Southwest United States. RLD has recently acquired a 40.625 acre site outside of Phoenix, Arizona. Zoning restrictions allow at most 8 units per acre. Three types of condominiums are planned: one, two, and three
4. Fruity Juices, Inc. produces five different flavors of fruit juice: apple, cherry, pomegranate, orange, and pineapple.Each batch of product requires processing in three departments (blending, straining, and bottling). The relevant data (per 1,000-gallon batches) are shown below.Time required in
3. Worley Fluid Supplies produces three types of fluidhandling equipment: control valves, metering pumps, and hydraulic cylinders. All three products require assembly and testing before they can be shipped to customers.Control Valve Metering Pump Hydraulic Cylinder Assembly time (min) 45 20 30
2. Burger Office Equipment produces two types of desks:standard and deluxe. Deluxe desks have oak tops and more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet
1. Korey is a business student at State U. She has just completed a course in decision models, which had a midterm exam, a final exam, individual assignments, and class participation. She earned an 86% on the midterm, 94% on the final, 93% on the individual assignments, and 85% on participation.
8. What is the transportation problem?
7. Discuss the implementation of optimization models on spreadsheets. Name some useful Excel tools which are helpful in this respect.
6. For each of the examples in this chapter, classify the constraints into the following categories. Are there any other types of constraints that do not fall into these categories?a. Simple boundsb. Limitationsc. Requirementsd. Proportional relationshipse. Balance constraints
5. What is a linear program?
4. Why do some common Excel functions cause difficulties when attempting to solve linear programs in Excel?
3. List the important guidelines to follow for modeling optimization problems on spreadsheets.
2. Describe the four main components of an optimization model. What are its constraints?
1. What is mean by optimization? What are some common scenarios where optimization models are used?
21. The “cobweb” model in economics assumes that the quantity demanded of a particular product in a specified time period depends on the price in that period.The quantity supplied depends on the price in the preceding period. Also, the market is assumed to be cleared at the end of each period.
20. Consider the continuous system dynamics model of medical rates in this chapter. A proposal has been made to improve the system by limiting medical rate and/or insurance rate increases to a maximum of 5% per year.Modify the spreadsheet to simulate each of the following scenarios and discuss the
19. An emergency room consists of four stations. Arrivals to the emergency room occur at a rate of four patients per hour and are assumed to follow an exponential distribution. Incoming patients are initially screened to determine their level of severity. Past data indicate that 5% of incoming
18. A retail store uses a ROP inventory system for a popular MP3 player that orders 40 units whenever the ROP of 25 is reached. The delivery time from the supplier has a mean of five days, with a standard deviation of 0.25 days. The time between customer demands is exponential with a mean of two
17. Computer monitors arrive to a final inspection station with a mean time between arrivals of 5.5 minutes (exponentially distributed). Two inspectors test the units, which takes an average of 10 minutes (again exponential).However, only 90% of the units pass the test; the remaining 10% are routed
16. A single clerk fills two types of orders. The first type arrives randomly, with a time between arrivals of 6 and 24 minutes; the second type of order has a time between arrivals of 45 and 75 minutes. It takes the clerk anywhere between 5 and 15 minutes to fill an order. Develop a SimQuick model
15. Prescriptions at a hospital pharmacy arrive at an average rate of 22 per hour, with exponentially distributed times between arrivals. One pharmacist can fill a prescription at a rate of 12 per hour, or one every five minutes, exponentially distributed. Develop a SimQuick model and use it to
14. A bank has an inside teller operation with two windows and a drive-through. Teller 2 works both inside and is responsible for the drive-through, while Teller 1 works only inside. Cars arrive to the drive-through uniformly every 5 to 15 minutes. Inside customers arrive uniformly every 10 to 20
13. A small manufacturing facility produces custom-molded plastic parts. The process consists of two sequential operations: mold/trim and assemble/package. Jobs arrive in batches at a mean rate of five jobs every two hours. For any job, the mold/trim process is exponential, with a mean of 15
12. A gasoline station near an outlet mall has two selfserve pumps and one full-serve pump that services only handicapped customers, which is 10% of the calling population. Customers arrive at an exponential rate of 1.6 customers per minute. Service times have discrete distributions as
11. Modify the factory simulation in Problem 10 to include two mold/trim servers (each with the original time distribution).How do your results change?
10. A small factory has two serial work stations: mold/trim and assemble/package. Jobs to the factory arrive at an exponentially distributed rate of one every 10 hours. Time at the mold/trim station is exponential,with a mean of seven hours. Each job proceeds next to the assemble/package station
9. A machine shop has a large number of machines that fail regularly. One repairperson is available to fix them.Each machine fails on average every three hours, with time between failures being exponential. Repair time(in minutes) has the distribution:Time Probability 15 0.1 30 0.2 45 0.3 50 0.4
8. People arrive at a self-service cafeteria on average every 15 seconds, exponentially distributed. There are two counters, entrées and drinks. Thirty percent of customers want entrées only, 60% go first to entrées then to drinks, and the remaining get only a drink. Service time at each counter
7. People arrive at a busy airport news kiosk at a rate that is uniformly distributed between five and ten seconds.Most people buy only one paper, which takes an average of six seconds, but may be as little as three or as much as nine seconds, and 20% buy two papers, which takes between six and
6. Complete the following table for a queuing simulation. Customer Arrival Time Service Time Start Time End Time Waiting Time Server Idle Time 1 1.1 0.6 2 2.2 1.1 m4 3 2.9 3.3. 3.7 1.0 5 4.9 0.8 61890 6.6 4.2 7 9.4 0.8 10.6 1.3. 11.1 0.1 13.3 3.8
5. A fast food store has a single server. Customers arrive at the store at the rate of six per hour according to a Poisson process. Serving times average four minutes according to an exponential distribution. What are the operating characteristics for this system?
4. A single teller serves the customers in a bank during the afternoon hours of 2 to 3 pm. The teller can serve a customer in an average of four minutes. Suppose that the arrival rates of customers are 10 customers per hour.a. Find the operating characteristics of the single teller queuing
3. A hair cutting saloon has a single barber who can serve a customer in an average of 20 minutes. Customers arrive in the saloon at an average rate of two per hour for getting a haircut this service.a. How long will a customer expect to wait before being served?b. On the average how many customers
2. Suppose students arrive during the office hours of a college professor according to a Poisson process with mean arrival rate l. The professor, who deals with his students one by one, has an exponentially distributed service time of ten per hour. Analyze how the average waiting time is expected
1. A grocery store checkout counter has a service rate of 45 per hour, exponentially distributed, with Poisson arrivals at the rate of 30 per hour. Find the operating characteristics of this system.
12. How does continuous simulation modeling differ from process simulation? Provide some practical examples different from the text where continuous simulation models might be used.
11. Explain the key features of SimQuick and how they are used in simulation models.
10. What is Little’s Law, and why is it important?
9. Explain the difference between steady-state and transient behavior in queuing systems.
8. Why do queues build up when the mean arrival rate equals the mean service rate?
7. List and define the major types of performance measures used in queuing analysis.
6. What is the purpose of process simulation? Name the tool which may be used to perform process simulation in Excel.
5. Explain the following terms:a. Calling populationb. Renegingc. Jockeyingd. Balkinge. Queue discipline
4. What is meant by operating characteristics? What do they measure?
3. Describe the standard assumptions for the serving characteristics in a queuing system.
2. What is an arrival process? Describe the most common arrival process used in practice.
1. What is a queuing system?
23. A college football team is trailing 14–0 late in the game.The team is getting close to making a touchdown. If they can score now, hold the opponent, and score one more time, they can tie or win the game. The coach is wondering whether to go for an extra-point kick or a two-point conversion
22. Consider the car rental insurance scenario in Problem 8.Use the approach described in this chapter to develop your personal utility function for the payoffs associated with this decision. Determine the decision that would result using the utilities instead of the payoffs. Is the decision
21. MJ Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse or a small one.Construction costs for the large facility are $8 million versus $5 million for the small facility. The profit (excluding
20. Hahn Engineering is planning on bidding on a job and often competes against a major competitor, Sweigart and Associates (S&A), as well as other firms. Historically, S&A has bid for the same jobs 80% of the time. If S&A bids on a job, the probability that Hahn Engineering will win it is 0.30. If
19. Drilling decisions by oil and gas operators involve intensive capital expenditures made in an environment characterized by limited information and high risk.A well site is dry, wet, or gushing. Historically, 50% of all wells have been dry, 30% wet, and 20% gushing. The value (net of drilling
18. Many automobile dealers advertise lease options for new cars. Suppose that you are considering three alternatives:1. Purchase the car outright with cash.2. Purchase the car with 20% down and a 48-month loan.3. Lease the car.Select an automobile whose leasing contract is advertised in a local
17. Dean Kuroff started a business of rehabbing old homes.He recently purchased a circa-1800 Victorian mansion and converted it into a three-family residence. Recently, one of his tenants complained that the refrigerator was not working properly. Since Dean’s cash flow was not extensive, he was
16. Perform a sensitivity analysis of the Midwestern Hardware scenario (Problem 15). Find the optimal order quantity and optimal expected profit for probabilities of a harsh winter ranging from 0.2 to 0.8 in increments of 0.2. Plot optimal expected profit as a function of the probability of a harsh
15. Midwestern Hardware must decide how many snow shovels to order for the coming snow season. Each shovel costs $15.00 and is sold for $29.95. No inventory is carried from one snow season to the next. Shovels unsold after February are sold at a discount price of $10.00. Past data indicate that
14. A patient arrives at an emergency room complaining of abdominal pain. The ER physician must decide on whether to operate or to place the patient under observation for a non-appendix-related condition. If an appendectomy is performed immediately, the doctor runs the risk that the patient does
13. An investor is considering a two-asset portfolio. Stock A has an expected return of $4.50 per share with a standard deviation of $1.00, while stock B has an expected return of $3.75 with a standard deviation of $0.75. The covariance between the two stocks is -0.35. Find the portfolio risk if:a.
12. Bev’s Bakery specializes in sourdough bread. Early each morning, Bev must decide how many loaves to bake for the day. Each loaf costs $0.75 to make and sells for $2.85.Bread left over at the end of the day can be sold the next for $1.00. Past data indicate that demand is distributed as
11. Mountain Ski Sports, a chain of ski equipment shops in Colorado, purchases skis from a manufacturer each summer for the coming winter season. The most popular intermediate model costs $150 and sells for $260.Any skis left over at the end of the winter are sold at the store’s half-price sale
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