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.b. What percentage of the time will Walker have only one bulb burning?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.5: Simulating Games Of Chance

Problem 41P: Consider the following card game. The player and dealer each receive a card from a 52-card deck. At...

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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?
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?
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?
A software firewall development company is selling a solution against distributed denial of service attacks (DDoS). the software solution looks at the IP address of all incoming packets and if it finds any address that accounts for more than 2% of the network traffic over the last hour, it installs an entry in the firewall (rule table) that blocks all packets from that IP address for 24 hours. the company is very happy and believes that this solution prevents DDOS attacks. a. is this a good solution for preventing DDOS (Yes or No)? b. give two reasons why it is a good solution or why it is not c. can this solution also be used to prevent LAND attacks? explain the answer
Same situation as in the previous two problems this time the magnet s mass is 5.68 kg and the magnetic force pulling it to the right is 170.9 N. The length of the cord is 1.70 m, and the ceiling is 2.98 m above the floor. Suppose that you cut the cord and the magnet falls to the floor while still being pulled to the right by the force of 170.9 N. How long will it take the magnet to hit the floor? 0.848 s 0.403 s 0.707 s 0.495 s
Bad simulations Explain why each of the followingsimulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to representthe number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a ran-dom digit, using an odd digit to represent a good shot and an even digit to represent a miss.c) Use random numbers from 1 through 13 to represent thedenominations of the cards in a five-card poker hand.
A study on ethics in the workplace by the Ethics Resource Center and Kronos, Inc., revealed that 35% of employees admit to keeping quiet when they see coworker misconduct. Suppose 70% of employees who admit to keeping quiet when they see coworker misconduct call in sick when they are well. In addition, suppose that 45% of the employees who call in sick when they are well admit to keeping quiet when they see coworker misconduct. If an employee is randomly selected, determine the following probabilities:a. The employee calls in sick when well and admits to keeping quiet when seeing coworker misconduct.b. The employee admits to keeping quiet when seeing coworker misconduct or calls in sick when well.c. Given that the employee calls in sick when well, he or she does not keep quiet when seeing coworker misconduct.d. The employee neither keeps quiet when seeing coworker misconduct nor calls in sick when well.e. The employee admits to keeping quiet when seeing coworker misconduct and does not…
Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.
ABCar Co is a new type of car company. They hire various subcontractors namely DesignCar Ltd., who designs the cars, ManuCar Inc., who manufactures the vehicles, and TestCar Co., who tests the cars before they are put into full production. Recently, ABCar Co has received many complaints about the failure of the braking system. There is a dispute between ABCar Co, DesignCar Ltd., ManuCar Inc., and TestCar Co. as to who is responsible for the problem and who must bear the cost to fix it. Referring to the dispute resolution mechanisms you explained in question 3 (a) (you don't need to reproduce the information), which dispute resolution mechanism would you select to resolve this dispute and why would you select it? Why would you reject the other ones?
Engineering student Bryan Springer has a high paying summer job as a forklift operator. This job enables him to attend university without having to take out any student loans. He was now staring at a 50-gallon drum filled with used machine coolant, wondering what he should do. Just moments ago, Bryan's supervisor, Max Morrison, told him to dump half of the used coolant down the drain. Bryan knew the coolant was toxic, and he mentioned this to Max. But Max was not swayed. Max: The toxins settle at the bottom of the drum. If you pour out half and dilute it with tap water while you're pouring it, there's no problem. Byran: I don't think that's going to work. Besides, isn't it against the law? Max: Look, kid, I don't have time for chat about a bunch of laws. If I spent my time worrying about every little regulation that comes along, I'd never get anything done -- and neither will you. Common sense is my rule. I just told you --Toxins settle at the bottom, and most of them will stay…