A piece of industrial machinery costs $48,000 to replace and has essentially no salvagevalue. Over the first five years of operation, maintenance costs amounted to $8,000. Ifthe maintenance cost rate is a linear function of time, what is the optimal age at whichto replace the machinery?
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A piece of industrial machinery costs $48,000 to replace and has essentially no salvage
value. Over the first five years of operation, maintenance costs amounted to $8,000. If
the maintenance cost rate is a linear function of time, what is the optimal age at which
to replace the machinery?
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- You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?Payoff Insurance Company charges a customeraccording to his or her accident history. A customer whohas had no accident during the last two years is charged a$100 annual premium. Any customer who has had anaccident during each of the last two years is charged a $400annual premium. A customer who has had an accident duringonly one of the last two years is charged an annual premiumof $300. A customer who has had an accident during the lastyear has a 10% chance of having an accident during thecurrent year. If a customer has not had an accident duringthe last year, there is only a 3% chance that he or she willhave an accident during the current year. During a givenyear, what is the average premium paid by a Payoffcustomer?
- 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?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?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?If a student attends every business analytics class, the probability of passing the course is 0.90; but if the student only attends randomly, then the probability of passing the course is 0.30. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.20 if the student has attended at random. Passing the course is worth 5 credits. Full-time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Draw a decision tree and use the decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the makeup exam and that the payoff for failing is equal to 0 credit. Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the student choose?
- A television network earns an average of $65 million each season from a hit program and loses an average of $25 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 30% turn out to be hits; the rest turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 65% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 40% chance that the market researchers will predict the program to be a hit. a. What is the maximum value of C that the network should be willing to pay the market research firm? If needed, round your answer to three decimal digits.A television network earns an average of $65 million each season from a hit program and loses an average of $25 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 30% turn out to be hits; the rest turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospective program and issue a report predicting whether the given program will end up being a hit. If the program is actually going to be a hit, there is a 65% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 40% chance that the market researchers will predict the program to be a hit. a. What is the maximum value of C that the network should be willing to pay the market research firm? If needed, round your answer to three decimal digits. b. Calculate and interpret EVPI for this decision problem. If needed, round your answer to one…Suppose the equilibrium price for good quality used cars is $20,000. And the equilibrium price for poor quality used cars is $10,000. Assume a potential used car buyer has imperfect information as to the condition of any given used car. Assume this potential buyer believes the probability a given used car is good quality is .60 and the probability a given used car is low quality is .40. Assume the seller has perfect information on all cars in inventory. If the seller sells the buyer a good quality car, what is the net-benefit to the seller? a. A net gain of $4,000. b. A net gain of $20,000. c. A net loss of $4,000. d. A net loss of $10,000.