Habard’s, a chain of hardware stores, sells a variety of tools and home repair items.One of their best wrenches sells for $5.50. Habard’s will include a three-year freereplacement warranty for an additional $1.50. The wrench is expected to be subject to heavy use and, based on past experience, will fail randomly at a rate of oneevery eight years. Is it worth purchasing the warranty?

Habard’s, a chain of hardware stores, sells a variety of tools and home repair items.One of their best wrenches sells for $5.50. Habard’s will include a three-year freereplacement warranty for an additional $1.50. The wrench is expected to be subject to heavy use and, based on past experience, will fail randomly at a rate of oneevery eight years. Is it worth purchasing the warranty?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 65P

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When Apple introduced its mobile payment system in 2014, the company was looking to leverage the popularity of its iPhone by adding more functionality and convenience for millions of customers. With Apple Pay, iPhone owners and Apple Watch wearers first enter their credit- or debit-card information, which Apple confirms with the banks. Once this information is on file, Apple creates a digital “token” that will be electronically transmitted to the retailer when an iPhone owner pays for something. To complete a purchase, the customer simply waves the phone or taps it at the checkout, uses the iPhone’s Touch or Face ID security to activate Apple Pay, and the phone instantly transfers the token as payment. Even though Apple Pay offers consumers the benefits of convenience and security, Apple knew it wouldn’t succeed without a large network of retailers, restaurants, and other businesses agreeing to accept its mobile payments. Among the earliest businesses to sign up with Apple was McDonald’s, which agreed to honor Apple Pay in its 14,000 U.S. restaurants and drive-through locations. “We serve 27 million customers every day. This is a clear and compelling business opportunity for us,” explained McDonald’s chief information officer. Compared with cash transactions, Apple Pay transactions cost McDonald’s a few pennies more to process because of bank fees. Yet the fast-food giant was willing to sign on because it saw competitive advantage and profit potential in wooing iPhone users interested in speedy checkout. Another early business supporter was Walgreens, the nationwide drug-store chain with 85 million customers enrolled in its frequent-buyer rewards program. Walgreens sells snacks, household products, and health and beauty items in addition to health-care products. Not only did Walgreens agree to accept Apple Pay at its checkout counters, but it was also the first U.S. retailer to add its rewards program to Apple Pay’s easy sign-on system. As a result, Walgreens’ customers tap twice at the checkout, once to activate the rewards account and display their savings, the second time to process the actual payment. By deciding to honor Apple Pay, Walgreens said it was “enabling a simple and convenient customer experience.” Several hundred thousand businesses had signed on to participate by the time Apple Pay launched in October 2014. Apple’s ongoing efforts to increase business participation paid off: Eighteen months later, the network of participating businesses topped 2 million, and major companies like Starbucks, Domino’s, and Crate & Barrel were preparing to participate. Eyeing international expansion, Apple also initiated talks with banks in China to bring Apple Pay to millions of iPhone users there. Today, Apple Pay is accepted at more than 50 percent of all U.S. retail locations and in many retail stores in twenty countries. Even though more consumers are making more mobile payments year after year, not every U.S. retailer is willing or able to work with Apple Pay. Some aren’t satisfied with the amount of consumer information that Apple Pay shares with participating merchants. Others would have to upgrade to new checkout technology for Apple Pay. Still others are locked into exclusive mobile payment deals with competing services. Today, mobile payments represent a small fraction of all purchase transactions, dwarfed by cash as well as by credit and debit payments. And Apple Pay faces strong competition from Google, Samsung, and others operating in the mobile-payment market. To remain a leader, Apple will have to keep signing more participating businesses and showing consumers the benefits of paying by iPhone or Apple Watch whenever they make a purchase. Which environmental influences on the decision process seem to have been most important to McDonald’s when it decided to honor Apple Pay?
When Apple introduced its mobile payment system in 2014, the company was looking to leverage the popularity of its iPhone by adding more functionality and convenience for millions of customers. With Apple Pay, iPhone owners and Apple Watch wearers first enter their credit- or debit-card information, which Apple confirms with the banks. Once this information is on file, Apple creates a digital token that will be electronically transmitted to the retailer when an iPhone owner pays for something. To complete a purchase, the customer simply waves the phone or taps it at the checkout, uses the iPhones Touch or Face ID security to activate Apple Pay, and the phone instantly transfers the token as payment. Even though Apple Pay offers consumers the benefits of convenience and security, Apple knew it wouldnt succeed without a large network of retailers, restaurants, and other businesses agreeing to accept its mobile payments. Among the earliest businesses to sign up with Apple was McDonalds, which agreed to honor Apple Pay in its 14,000 U.S. restaurants and drive-through locations. We serve 27 million customers every day. This is a clear and compelling business opportunity for us, explained McDonalds chief information officer. Compared with cash transactions, Apple Pay transactions cost McDonalds a few pennies more to process because of bank fees. Yet the fast-food giant was willing to sign on because it saw competitive advantage and profit potential in wooing iPhone users interested in speedy checkout. Another early business supporter was Walgreens, the nationwide drug-store chain with 85 million customers enrolled in its frequent-buyer rewards program. Walgreens sells snacks, household products, and health and beauty items in addition to health-care products. Not only did Walgreens agree to accept Apple Pay at its checkout counters, but it was also the first U.S. retailer to add its rewards program to Apple Pays easy sign-on system. As a result, Walgreens customers tap twice at the checkout, once to activate the rewards account and display their savings, the second time to process the actual payment. By deciding to honor Apple Pay, Walgreens said it was enabling a simple and convenient customer experience. Several hundred thousand businesses had signed on to participate by the time Apple Pay launched in October 2014. Apples ongoing efforts to increase business participation paid off: Eighteen months later, the network of participating businesses topped 2 million, and major companies like Starbucks, Dominos, and Crate Barrel were preparing to participate. Eyeing international expansion, Apple also initiated talks with banks in China to bring Apple Pay to millions of iPhone users there. Today, Apple Pay is accepted at more than 50 percent of all U.S. retail locations and in many retail stores in twenty countries. Even though more consumers are making more mobile payments year after year, not every U.S. retailer is willing or able to work with Apple Pay. Some arent satisfied with the amount of consumer information that Apple Pay shares with participating merchants. Others would have to upgrade to new checkout technology for Apple Pay. Still others are locked into exclusive mobile payment deals with competing services. Today, mobile payments represent a small fraction of all purchase transactions, dwarfed by cash as well as by credit and debit payments. And Apple Pay faces strong competition from Google, Samsung, and others operating in the mobile-payment market. To remain a leader, Apple will have to keep signing more participating businesses and showing consumers the benefits of paying by iPhone or Apple Watch whenever they make a purchase. Which of the four categories of business markets is Apple Pay best suited for, and why?
United Electric (UE) sells refrigerators for $400 with a one-year warranty. The warranty works as follows. If any part of the refrigerator fails during the first year after purchase, UE replaces the refrigerator foran average cost of $100. As soon as a replacement is made, another one-year warranty period begins for the customer. If a refrigerator fails outside the warranty period, we assume that the customer immediatelypurchases another UE refrigerator. Suppose that the amount of time a refrigerator lasts follows a normal distribution with a mean of 1.8 years and a standard deviation of 0.3 year.a. Estimate the average profit per year UE earns from a customer.b. How could the approach of this problem be used to determine the optimal warranty period?
A producer of pocket calculators estimates that the calculators fail at a rate of oneevery five years. The calculators are sold for $25 each with a one-year freereplacement warranty but can be purchased from an unregistered mail-ordersource for $18.50 without the warranty. Is it worth purchasing the calculator withthe warranty? For Problem 37, what length of period of the warranty equates the replacementcosts of the calculator with and without the warranty?
Zemansky’s sells tires with a pro rata warranty. The tires are warranted to deliver50,000 miles with the rebate based on the remaining tread on the tire. The tires failon the average after 35,000 miles of wear. Suppose the tires sell for $50 each withthe warranty. If failures occur completely at random, what would be a consistentprice for the tires if no warranty were offered?
A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost? Support your answer with drawing a decision tree and provide your calculation.
A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Construct a decision tree to help the farmer make his decision. What should he do? Explain your answer. Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of…
A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 a. Construct a decision tree to help the farmer make his decision. What should he do? b. Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. c. Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of a freeze occurring…
A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Construct a decision tree to help the farmer make his decision. What should he do?
Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.b. What percentage of the time will Walker have only one bulb burning?
Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.c. Is there any advantage of James’s strategy over Smith’s?
Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.a. Over a 10-year period, how many bulbs, on average, will each neighbor require?