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 from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customer demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 90% of customer demand.
> Foxcomp, an electronics and computer manufacturer with a global supply chain, wants to add a new supplier for some of its component parts, and the suppliers it’s considering are in Taiwan, India, Thailand, and the Philippines. As part o
> Assume that the probabilities of demand in Problem 30 are no longer valid; the decision situation is now one without probabilities. Determine the best number of boxes of cards to stock, using the following decision criteria. a. Maximin b. Maximax c. Hurw
> The Palm Garden Greenhouse specializes in raising carnations that are sold to florists. Carnations are sold for $3.00 per dozen; the cost of growing the carnations and distributing them to the florists is $2.00 per dozen. Any carnations left at the end o
> The manager of the greeting card section of Mazey’s department store is considering her order for a particular line of Christmas cards. The cost of each box of cards is $3; each box will be sold for $5 during the Christmas season. After
> Stevie Stone, a bellhop at the Royal Sundown Hotel in Atlanta, has been offered a management position. Although accepting the offer would assure him a job if there was a recession, if good economic conditions prevailed, he would actually make less money
> The Loebuck Grocery must decide how many cases of milk to stock each week to meet demand. The probability distribution of demand during a week is shown in the following table: Each case costs the grocer $10 and sells for $12. Unsold cases are sold to a l
> Two area hospitals have jointly initiated several planning projects to determine how effectively their emergency facilities can handle disaster-related situations at nearby Tech University. These disasters could be weather related (such as a tornado), a
> 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 $.
> Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. producer of full-sized cars, and from a truck company. The success of each type of
> In Problem 13, the Place-Plus real estate development firm has hired an economist to assign a probability to each direction interest rates may take over the next 5 years. The economist has determined that there is a .50 probability that interest rates wi
> A global economist hired by Microcomp, the U.S.-based computer manufacturer in Problem 12, estimates that the probability that the economic and political climate overseas and in Mexico will decline during the next 5 years is .40, the probability that it
> In Problem 11, the Tech coaches have reviewed game films and have determined the following probabilities that State will use each of its defenses: a. Using expected value, rank Tech’s plays from best to worst. b. During the actual game,
> In Problem 10, Ann Tyler, with the help of a financial newsletter and some library research, has been able to assign probabilities to each of the possible interest rates during the next year, as follows: Using expected value, determine her best investmen
> An investor must decide between two alternative investments—stocks and bonds. The return for each investment, given two future economic conditions, is shown in the following payoff table: What probability for each economic condition wou
> The financial success of the Downhill Ski Resort in the Blue Ridge Mountains is dependent on the amount of snowfall during the winter months. If the snowfall averages more than 40 inches, the resort will be successful; if the snowfall is between 20 and 4
> The Miramar Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes, as shown in the following payoff table
> The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive-up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the
> Bob and Carol Packer operate a successful outdoor-wear store in Vermont called Northwoods Backpackers. They stock mostly cold weather outdoor items such as hiking and backpacking clothes, gear, and accessories. They established an excellent reputation th
> Allen Abbott has a wide-curving, uphill driveway leading to his garage. When there is a heavy snow, Allen hires a local carpenter, who shovels snow on the side in the winter, to shovel his drive- way. The snow shoveler charges $30 to shovel the driveway.
> A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather for
> A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each pur
> In problem 15, if the probabilities that Mill Mountain coffee house will use marketing strategies A, B, and C are 0.25, 0.45, and 0.30, respectively, compute the expected value for each of Startrak’s strategies and select the best one.
> Two coffee house chains, Startrak and Mill Mountain, dominate the Columbus market. Startrak has developed three new marketing strategies, 1, 2, and 3, for the fall season, which include various combinations of media and print advertising and promotions.
> The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Byrd, Rayneal Oâ&
> Place-Plus, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, b
> Microcomp is a U.S.-based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in either South Korea, China, Taiwan, the Philippines, or Mexico. It will take approximately 5 years to build the necessar
> The Tech football coaching staff has six basic offensive plays it runs every game. Tech has an upcoming game against State on Saturday, and the Tech coaches know that State employs five different defenses. The coaches have estimated the number of yards T
> 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
> 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 Evergreen Fertilizer Company produces two types of fertilizers, Fastgro and Super Two. The company has developed the following nonlinear programming model to determine the optimal number of bags of Fastgro (x1) and Super Two (x2) that it must produce
> 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:
