50. Applicational Materials sells several pieces of equipment used in the manufactureof silicon-based microprocessors. In 2003 the company filled 130 orders for modela55212. Suppose that the machines fail according to a Weibull law. In particular,the cumulative distribution function F(t) of the time until failure of any machineAppendix 13–A 793is given byF(t) = 1 – e-0.04751 2for all t> 0,where t is in years.a. What is the failure rate function for this piece of equipment?b. Of the original 130 sold in 2003, how many machines would one expect would notexperience a breakdown before January 2007? Assume for the sake of simplicitythat all the machines were sold on January 1, 2003.c. Using the results of part (a), estimate the fraction of machines that have survived10 years of use that will break down during the 11th year of operation [or you maycompute this directly if you did not get the answer to part (a)].

a) Calculation of function failure rate r(t) The known cumulative distribution function F(t) =…

Answered: 50. Applicational Materials sells…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 66P: Rework the previous problem for a case in which the one-year warranty requires you to pay for the...

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53. Why is the RISKCORRMAT function necessary?How does @RISK generate random inputs by default,that is, when RISKCORRMAT is not used
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?
Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + βu(C2) Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin t r a d e s a t P1 > 0 in the first period and is expected to trade at P ̃2 in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the P ̃2? Is P ̃2 a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?
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.
Suppose that $100 is invested at the beginning of a year. Which (if either) of the following methods of growing the investment results in a larger amount at the end of the year? (i) The investment grows at an interest rate of 4% per year, compounded continuously.(ii) The investment grows at an instantaneous growth rate of 4% per year. method (i) method (ii) Both methods produce the same amount.
#17FAVORABLE UNFAVORABLEMARKET MARKETEQUIPMENT ( $) ($)Sub 100 300,000 –200,000Oiler J 250,000 –100,000Texan 75,000 –18,000For example, if Ken purchases a Sub 100 and ifthere is a favorable market, he will realize a profitof $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. ButKen has always been a very optimistic decisionmaker.(a) What type of decision is Ken facing?(b) What decision criterion should he use?(c) What alternative is best? #18Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob iscredited with making the company a financial success. Bob is vice president of finance. Bob attributeshis success to his pessimistic attitude about business and the oil industry. Given the information fromProblem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should Bobuse, and what alternative…
If a stock’s intrinsic value exceeds its market price, then it is __________ and should be __________. A. overvalued, sold B. overvalued, bought C. undervalued, bought D. undervalued, sold
Suppose that Pizza King and Noble Greek stopadvertising but must determine the price they will chargefor each pizza sold. Pizza King believes that Noble Greek’sprice is a random variable D having the following massfunction: P(D $6) .25, P(D $8) .50, P(D $10) .25. If Pizza King charges a price p1 and NobleGreek charges a price p2, Pizza King will sell 10025( p2 p1) pizzas. It costs Pizza King $4 to make a pizza.Pizza King is considering charging $5, $6, $7, $8, or $9 fora pizza. Use each decision criterion of this section todetermine the price that Pizza King should charge.
A building contains 1000 lightbulbs. Each bulb lastsat most five months. The company maintaining thebuilding is trying to decide whether it is worthwhileto practice a “group replacement” policy. Under agroup replacement policy, all bulbs are replaced everyT months (where T is to be determined). Also, bulbsare replaced when they burn out. Assume that it costs$0.05 to replace each bulb during a group replacementand $0.20 to replace each burned-out bulb if it isreplaced individually. How would you use simulationto determine whether a group replacement policy isworthwhile?
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
4. A publisher prints copies of a popular weekly tabloid for distribution and sale. The fixed costs are $500 per print run, with each copy printed costing an additional $0.40. If C(q) is the cost function (in $) of the price of the print run as a function of copies printed, what is the formula for C(q)? Select one: a. C(q) = 500 + 0.4q b. C(q) = 500q + 0.4 c. C(q) = (500 + 0.4)q d. C(q) = 500 - 0.4q e. C(q) = 500q - 0.4 5. A hot dog vendor sells an average of 50 hot dogs during a Little League baseball game. If the sales are Normally distributed with a standard deviation of 7 hot dogs, what is the probability the vendor will sell between 45 and 65 hot dogs? Select one: a. 74.50% b. 92.36% c. 99.78% d. 174.50% e. 2.14 f. -0.71 g. 0.71
Michelle owns a house in which she keeps valuables worth 100,000 which can get stolen with probability 1%. She can purchase coverage C of the amount C ∈ [0; 100,000] at premium π = 0.05 dollars for each dollar covered. Her Bernouilli utility function is u(w) = ln(w). Assume she has no other assets. 1. Set up her maximization problem. 2. How much insurance will she choose to buy? 3. How much profits does the insurance company earn on insuring Michelle? 4. Does the fact that the insurance company earn profits mean that Michelle is worse off com-pared to the situation in which she is not insured? Explain what is happening. 5. How much insurance will she buy if insurance companies charge an actuarially fair insurance rate?

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