Question: The Evergreen Fertilizer Company produces two types

> Ann Tyler has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after 1 year is primarily dependent on the interest rate during the next year. The rate is currently 7%, and Ann a

> The copy center at the college of business at State University has become an increasingly contentious item among the college administrators. The department heads have complained to the associate dean about the long lines and waiting times for their secre

> A farmer in Iowa is considering either leasing some extra land or investing in savings certificates at the local bank. If weather conditions are good next year, the extra land will give the farmer an excellent harvest. However, if weather conditions are

> A new county hospital is attempting to determine whether it needs to add a particular specialist to its staff. Five percent of the general hospital population in the county contracts the illness the specialist would treat. If 12 patients check into the h

> An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck 1 year are defective. It has contacted the owners of these vehicles and asked them to return their trucks to the dealer to check the t

> A polling firm is taking a survey regarding a proposed new law. Of the voters polled, 30% are in favor of the law. If 10 people are surveyed, what is the probability that four will indicate that they are opposed to the passage of the new law?

> A manufacturing company has 10 machines in continuous operation during a workday. The probability that an individual machine will break down during the day is .10. Determine the probability that during any given day three machines will break down.

> The quality control process at a manufacturing plant requires that each lot of finished units be sampled for defective items. Twenty units from each lot are inspected. If five or more defective units are found, the lot is rejected. If a lot is known to c

> Geo-net, a cellular phone company, has collected the following frequency distribution for the length of calls outside its normal customer roaming area: The sample mean (x) for this distribution is 14.3 minutes, and the sample standard deviation is 3.7 mi

> The department of management science at Tech has sampled 250 of its majors and compiled the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester: The sample mean (x) for this distribution is 2.5, and the sam

> Employees in the textile industry can be segmented as follows: a. Determine the probability of each event in this distribution. b. Are the events in this distribution mutually exclusive? Explain. c. What is the probability that an employee is male? d. Is

> The state of Virginia has implemented a Standards of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their

> WestCom Systems Products Company develops computer systems and software products for commercial sale. Each year it considers and evaluates a number of different R&D projects to undertake. It develops a road map for each project, in the form of a

> In the novel Around the World in 80 Days by Jules Verne, Phileas T. Fogg wagered four of his fellow members of the Reform Club in London £5,000 apiece that he could travel around the world in 80 days. This would have been an astounding feat

> The owner of Gilley’s Ice Cream Parlor has noticed that she sells more ice cream on hotter days during the summer, especially on days when the temperature is 85°F or higher. To plan how much ice cream to stock, she would like

> Agnes Hammer is a senior majoring in management science. She has been interviewing with several companies for a job when she graduates, and she is curious about what starting salary offers she might receive. There are 140 seniors in the graduating class

> The Palace Hotel believes its customers may be waiting too long for room service. The hotel operations manager knows that the time for room service orders is normally distributed, and he sampled 10 room service orders during a 3-day period and timed each

> The associate dean in the college of business at Tech is going to purchase a new copying machine for the college. One model he is considering is the Zerox X10. The sales representative has told him that this model will make an average of 125,000 copies,

> Erin Richards is a junior at Central High School, and she has talked to her guidance counselor about her chances of being admitted to Tech after her graduation. The guidance counselor has told her that Tech generally accepts only those applicants who gra

> Students admitted in the decision science major of a public university are normally distributed with a mean of 150 and standard deviation of 15 in the quantitative section of GRE. The university admitted 250 students. Those who earned above 168 in the qu

> Lauren Moore, a professor in management science, is computing her final grades for her introductory management science class. The average final grade is a 63, with a standard deviation of 10. Professor Moore wants to curve the final grades according to a

> The owner of Western Clothing Company has determined that the company must sell 670 pairs of denim jeans each month to break even (i.e., to reach the point where total revenue equals total cost). The company’s marketing department has estimated that mont

> The manager of the local National Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder fro

> Downhill Ski Resort in Colorado has accumulated information from records of the past 30 winters regarding the measurable snowfall. This information is as follows: a. Determine the probability of each event in this frequency distribution. b. Are all the e

> The Carolina Cougars is a major league baseball expan- sion team beginning its third year of operation. The team had losing records in each of its first 2 years and finished near the bottom of its division. However, the team was young and generally compe

> A warehouse distributor of carpet keeps 6,000 yards of deluxe shag carpet in stock during a month. The average demand for carpet from the stores that purchase from the distributor is 4,500 yards per month, with a standard deviation of 900 yards. What is

> The Polo Development Firm is building a shopping center. It has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months, with a standard

> The monthly demand for a product is normally distributed, with a mean of 700 units and a standard deviation of 200 units. What is the probability that demand will be greater than 900 units in a given month?

> The weight of bags of fertilizer is normally distributed, with a mean of 50 pounds and a standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds?

> The grade point average of students at a university is normally distributed, with a mean of 2.6 and a standard deviation of 0.6. A recruiter for a company is interviewing students for summer employment. What percentage of the students will have a grade p

> The life of an electronic transistor is normally distributed, with a mean of 500 hours and a standard deviation of 80 hours. Determine the probability that a transistor will last for more than 400 hours.

> The time interval between machine breakdowns in a manufacturing firm is defined according to the following probability distribution: Determine the cumulative probability distribution and compute the expected time between machine breakdowns.

> The Jefferson High School Band Booster Club has organized a raffle. The prize is a $6,000 car. Two thousand tickets to the raffle are to be sold at $1 apiece. If a person purchases four tickets, what will be the expected value of the tickets?

> An investor is considering two investments, an office building and bonds. The possible returns from each investment and their probabilities are as follows: Using expected value and standard deviation as a basis for comparison, discuss which of the two in

> An investment firm is considering two alternative investments, A and B, under two possible future sets of economic conditions, good and poor. There is a .60 probability of good economic conditions occurring and a .40 probability of poor economic conditio

> Mountain States Electric Service is an electrical utility company serving several states in the Rocky Mountains region. It is considering replacing some of its equipment at a generating substation and is attempting to decide whether it should replace an

> A gambler in Las Vegas is cutting a deck of cards for $1,000. What is the probability that the card for the gambler will be the following? a. A face card b. A queen c. A spade d. A jack of spades

> A market in Boston orders oranges from Florida. The oranges are shipped to Boston from Florida by railroad, truck, or airplane; an order can take 1, 2, 3, or 4 days to arrive in Boston once it is placed. The following probabilities have been assigned to

> The following probabilities for grades in management science have been determined based on past records: The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.

> The Ramshead Pub sells a large quantity of beer every Saturday. From past sales records, the pub has determined the following probabilities for sales: Compute the expected number of barrels that will be sold on Saturday.

> A metropolitan school system consists of two districts, east and west. The east district contains 35% of all students, and the west district contains the other 65%. A vocational aptitude test was given to all students; 10% of the east district students f

> A service station owner sells Goodroad tires, which are ordered from a local tire distributor. The distributor receives tires from two plants, A and B. When the owner of the service station receives an order from the distributor, there is a .50 probabili

> 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%, and the central district contains 35%. A minimum-competency test was given to all studen

> A retail outlet receives radios from three electrical appliance companies. The outlet receives 20% of its radios from A, 40% from B, and 40% from C. The probability of receiving a defective radio from A is .01; from B, .02; and from C, .08. a. Develop a

> The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple

> Two law firms in a community handle all the cases dealing with consumer suits against companies in the area. The Abercrombie firm takes 40% of all suits, and the Olson firm handles the other 60%. The Abercrombie firm wins 70% of its cases, and the Olson

> Steeley Associates, Inc., a property development firm, purchased an old house near the town square in Concord Falls, where State University is located. The old house was built in the mid-1800s, and Steeley Associates restored it. For almost a decade, Ste

> 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, or emphysema,

> Indicate which of the following probabilities are objective and which are subjective. (Note that in some cases, the probabilities may not be entirely one or the other.) a. The probability of snow tomorrow b. The probability of catching a fish c. The prob

> The Beaver Creek Pottery Company has developed the following nonlinear programming model to determine the optimal number of bowls (x1) and mugs (x2) to produce each day: Determine the optimal solution to this nonlinear programming model.

> The Rainwater Brewery produces beer, which it sells to distributors in barrels. The brewery incurs a monthly fixed cost of $12,000, and the variable cost per barrel is $17. The brewery has developed the following profit function and demand constraint: ma

> Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering mass- producing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be $25,000, while labor, materials, packaging, and s

> The Grady Tire Company recaps tires. The weekly fixed cost is $2,500, and the variable cost per tire is $9. Price is related to demand, according to the following linear equation: v = 200 - 4.75 p Develop the nonlinear profit function for the tire compan

> The Rolling Creek Textile Mill makes denim. The monthly fixed cost is $8,000, and the variable cost per yard of denim is $0.35. Price is related to demand, according to the following linear equation: v = 17,000 - 5,666 p Develop the nonlinear profit func

> The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost per barrel is $16. Price is related to demand, according to the following linear equation: v = 75,000 - 1,153.8 p Develop the nonlinear profit function for the

> The Accentuate Consulting Firm has eight projects for which it has contracted with clients to develop computer systems and software. The firm has 35 team members it can assign to the projects. The firm has developed the following profit functions for eac

> The Valley Swim Club has 300 stockholders, each holding one share of stock in the club. A share of club stock allows the shareholder’s family to use the club’s heated outdoor pool during the summer, upon payment of ann

> Mark Decker has identified four stocks for his portfolio, and he wants to determine the percent- age of his total available funds he should invest in each stock. The alternative stocks include an Internet company, a computer software company, a computer

> An investment adviser is helping a couple plan a retirement portfolio. The adviser has recommended three stocks—Allied Electronics, Bank United, and Consolidated Computers. Following are the annual return and variance for each stock and

> Graphically illustrate the profit curve developed in Problem 1. Indicate the optimal price and the maximum profit per month.

> Tech wants to locate the best site for a new student center and athletic complex. The university administration would like to know what the best location is relative to the four main concentrations of student housing and classroom activity on campus. The

> A company specializing in air conditioners wants to setup a distribution center in India. The company sells its products through six retail outlets located in the following cities in India: Chennai, Mumbai, Bangalore, New Delhi, Kolkata, and Vizag. The l

> A farmer prepares his land for plantation during the rainy season. He has right-angled triangle shaped land with length (b) and width (w). Since his land is close to a forest, forest animals some- times damage his crops. To ward off the animals, he plans

> The Metro Police Department has partitioned the city into four quadrants. The department has 20 police patrol cars available for each shift per day to assign to the quadrants. The department wants to assign patrol cars to the quadrants during a shift so

> A turbine is designed for generating electricity. During electricity generation, the turbine is subject to very high temperature. This high temperature and the speed of the turbine affects the sealing property. The turbine uses gasket and lubricating oil

> Metro Telcom Systems develops, sells, and installs computer systems. The company has divided its customer base into five regions, and it has 15 representatives who sell and install the company’s systems. The company wants to allocate sa

> Interpret the meaning of the Lagrange multiplier in Problem 12.

> American International Automotive Industries (AIAI) manufactures engine, transmission, and chassis parts for manufacturers and repair companies in the United States, South America, Canada, Mexico, Asia, and Europe. The company transports parts to its for

> The Riverwood Paneling Company makes two kinds of wood paneling: Colonial and Western. The company has developed the following nonlinear programming model to determine the optimal number of sheets of Colonial paneling (x1) and Western paneling (x2) to pr

> In the investment portfolio selection model in this chapter, what if Jessica Todd decided that she wanted to maximize her return while incurring a portfolio variance of no more than 0.020? Analyze this scenario by using the Excel spreadsheet in Exhibit 1

> The Rolling Creek Textile Mill produces denim and brushed cotton cloth. The company has developed the following nonlinear programming model to determine the optimal number of yards of denim (x1) and brushed cotton (x2) to produce each day to maximize pro

> The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2 p Develop the nonli

> Solve the following goal programming model by using the computer:

> Solve the following goal programming model graphically and by using the computer:

> Solve the following goal programming model graphically and by using the computer:

> Select four fast-food restaurants (e.g., McDonald’s, Burger King, Wendy’s, Domino’s, or local restaurants) in your area, and develop a scoring model that includes decision criteria, weights, and grades to rank the restaurants from best to worst.

> Suntrek manufactures denim jeans, which it sells to clothing retailers around the world. It wants to construct a new warehouse and distribution center in Asia to serve emerging markets there. It has identified potential sites in the port cities of Shangh

> As part of an aggressive expansion plan, StarTrack Coffee is planning to open three new retail stores in the city. The following table shows the location factors it considers to be important indicators of future profitability and how management has grade

> State University has increased its tuition for in-state and out-of-state students in each of the past 5 years to offset cuts in its budget allocation from the state legislature. The university administration always thought that the number of applications

> A study conducted on four brands of computers resulted in the following comparison matrix. The factors considered are the speed of processing (1), storage capacity (2), after sales service (3), and cost (4). a. Determine the priorities for the considered

> Robin Dillon has recently accepted a new job in the Washington, DC, area and has been hunting for a condominium to purchase. From friends and coworkers she has compiled a list of five possible condominium complexes that she might move into. The following

> The Barrett Textile Mill was checked by inspectors enforcing Occupational Safety and Health Administration (OSHA) codes. The inspectors found violations in four categories: hazardous materials, fire protection, hand-powered tools, and machine guarding. I

> The Carter family wants to purchase a time-share condominium for 1 week during the summer in Hilton Head, South Carolina. There are many resort complexes from which to choose, and the Carters have narrowed their list to five. They have graded their choic

> Following an all-star school soccer career, Kelly Williams has been offered scholarships to five universities. She has had a difficult time making a decision and has decided to use a scoring model to help evaluate the different offers. The following tabl

> State University is to construct a new student center and athletic complex that will include a bookstore, a post office, theaters, a market, a minimall, meeting rooms, a swimming pool, and weight and exercise rooms. The university administration has hire

> In Problem 38 Ben Cheery, the Sox general manager, also wants to use a scoring model to deter- mine which player(s) he might sign to a free agent contract for the coming baseball season. The following table shows a weighted list of criteria he has develo

> The Dynaco Manufacturing Company is to build a new plant to make ring bearings (used in automobiles and trucks). The site selection team is evaluating three sites, and it has graded the important weighted criteria for each as follows: Develop a scoring m

> Arsenal Electronics is to construct a new $1.2 billion semiconductor plant and has selected four small towns in the Midwest as potential sites. The important decision criteria and grades for each town are as follows: Develop a scoring model to determine

> Select four new models of cars you might like to purchase. Using AHP and your own preferences, rank your selections according to the following criteria: price, style/appearance, reliability/ maintenance, engine size, gas mileage, safety, and features/opt

> Suntrek is a global denim fabric and jeans manufacturer. It purchases raw, baled cotton from locations around the world (primarily the United States and Mexico) and ships it (in containers) to various factories it operates to manufacture denim fabric and

> Check the pairwise comparison in Problem 48 for consistency.

> Balston Healthcare operates three hospitals and a number of clinics in its citywide network. It is planning to open a new wellness center and clinic facility that focuses on geriatric clients in one of four suburbs. The following table shows the weighted

> For Problem 49, check the consistency of the pairwise comparison matrices for all four criteria and the criteria.

> The Growall Fertilizer Company produces three types of fertilizer—Supergro, Dynaplant, and Soilsaver. The company has the capacity to produce a maximum of 2,000 tons of fertilizer in a week. It costs $800 to produce a ton of Supergro, $1,500 for Dynaplan

> Labran Jones has played for the Cleveland professional basketball team for the past eight seasons and has established himself as one of the top players in the league. He has recently become a free agent, meaning he can sign a new contract with Cleveland

> A state university interviewed three candidates (A, B, C) for a faculty position in the department of decision sciences. The university selects the best candidate based on education (Ed), experience (Ex), and references (Re). The search committee has pre

> Check the pairwise comparison in Problem 46 for consistency.

> An undergraduate student of decision sciences wants to buy a mobile. He mainly focuses on three criteria: cost, battery life, and features. He has finalized three models of phones (M1, M2, and M3). Using his knowledge of AHP, he has created pairwise comp

> For Problem 44, develop your own pairwise comparisons for and among the criteria using your own knowledge of Civil War history and any Internet research you might perform, and develop your own AHP ranking of the four generals.

> The four most famous generals during the American Civil War were Ulysses S. Grant, William Tecumseh Sherman, Robert E. Lee, and Stonewall Jackson. Historians have always debated who the greatest general from among these four was. Following are the pairwi