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?
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Zemansky’s sells tires with a pro rata warranty. The tires are warranted to deliver
50,000 miles with the rebate based on the remaining tread on the tire. The tires fail
on the average after 35,000 miles of wear. Suppose the tires sell for $50 each with
the warranty. If failures occur completely at random, what would be a consistent
price for the tires if no warranty were offered?
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- Rework the previous problem for a case in which the one-year warranty requires you to pay for the new device even if failure occurs during the warranty period. Specifically, if the device fails at time t, measured relative to the time it went into use, you must pay 300t for a new device. For example, if the device goes into use at the beginning of April and fails nine months later, at the beginning of January, you must pay 225. The reasoning is that you got 9/12 of the warranty period for use, so you should pay that fraction of the total cost for the next device. As before, how-ever, if the device fails outside the warranty period, you must pay the full 300 cost for a new device.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?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?
- Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 20 percent are returned. If nine rings are sold today, what is the probability that fewer than four will be returned? A- 0.914 B- 0.962 C- 0.923 D- 0.935A hardware company sells a lot of low-cost, high volume products. For one such product, it is equally likely that annual unit sales will be low or high. If sales are low (30,000), the company can sell the product for $20 per unit. If sales are high (70,000), a competitor will enter and the company will be able to sell the product for only $15 per unit. The variable cost per unit has a 20% chance of being $10, a 60% chance of being $11, and a 20% chance of being $12. Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expected annual profit.b. Find a 95% interval for the company’s annual profit, that is, an interval such that about 95% of the actual profits are inside it.c. Now suppose that annual unit sales, variable cost, and unit price are equal to their respective expected values—that is, there is no uncertainty. Determine the company’s annual profit for this scenario. d. Can you conclude from the results in parts a and c that the expected profit from a…Cassette tapes are still used in some handheld recording devices and in less expensive portable musical instrument recording devices. The desired speed of a cassette tape is 1.900 inches per second. Any deviation from this value causes a change in pitch and tempo and thus poor sound quality. Suppose that adjusting the tape speed under warranty when a customer complains and returns a device costs a manufacturer $20. Based on past information, the company knows the average customer will return a device if the tape speed is off the target by at least 0.200 inches per second; in other words, when the speed is either 2.100 or 1.700. Suppose that a technician tests the tape speed prior to packaging and can adjust the speed to the target of 1.900 at a cost of $6. What should the economic specification limit be? The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. Questions 1. In the Taguchi…
- Cassette tapes are still used in some handheld recording devices and in less expensive portable musical instrument recording devices. The desired speed of a cassette tape is 1.900 inches per second. Any deviation from this value causes a change in pitch and tempo and thus poor sound quality. Suppose that adjusting the tape speed under warranty when a customer complains and returns a device costs a manufacturer $20. Based on past information, the company knows the average customer will return a device if the tape speed is off the target by at least 0.200 inches per second; in other words, when the speed is either 2.100 or 1.700. Suppose that a technician tests the tape speed prior to packaging and can adjust the speed to the target of 1.900 at a cost of $6. What should the economic specification limit be? The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. Question 4. What are the…Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table: For example, the probability of getting a batch of tests that are 1% defective from Winter Park Technology is .70. Because Kellogg orders 10,000 tests per order, this would mean that there is a .70 probability of getting 100 defective tests out of the 10,000 tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Winter Park. a) Develop a decision tree. b) Which supplier should Kellogg use?Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table: For example, the probability of getting a batch of tests that are 1% defective from Winter Park Technology is .70. Because Kellogg orders 10,000 tests per order, this would mean that there is a .70 probability of getting 100 defective tests out of the 10,000 tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Winter Park. a) Develop a Decision Treeb) Which supplier should Kellog use? Percent Defective Probability for Winter Park Technology Probability for Dayton Enterprises 1 0.70 0.30 3 0.20 0.30 5 0.10 0.40
- A collection of 30 Christmas tree lights are arranged in a pure series circuit; that is, ifone of the lights burns out, then the entire string goes out. Suppose that each light failscompletely at random at a rate of one failure every year. What is the probability that thelights will burn from the beginning of Christmas Eve (December 24) to the end of NewYear’s Day (January 1) without failure?A producer of pocket calculators estimates that the calculators fail at a rate of one every five years. The calculators are sold for $25 each with a one-year free replacement warranty but can be purchased from an unregistered mail-order source for $18.50 without the warranty. What length of period of the warranty equates the replacement costs of the calculator with and without the warranty?See how sensitive the results in Example 11.2 are to the following changes. For each part, make the change indicated, run the simulation, and comment on any differences between your outputs and the outputs in the example. a. The cost of a new camera is increased to $500. b. The warranty period is decreased to one year. c. The terms of the warranty are changed. If the cam- era fails within one year, the customer gets a new camera for free. However, if the camera fails between 1 year and 1.5 years, the customer pays a pro rata share of the new camera, increasing linearly from 0 to full price. For example, if it fails at 1.2 years, which is 40% of the way from 1 to 1.5, the customer pays 40% of the full price. d. The customer pays $50 up front for an extended warranty. This extends the warranty to three years. This extended warranty is just like the original, so that if the camera fails within three years, the customer gets a new camera for free.