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Department of Business and EconomicsCollege of Graduate Studies and ResearchCalifornia University of PennsylvaniaCalifornia, PA 15419BUS 771 Quantitative MethodsDr. Edmund MateckiExam 3Fall 2019NAME: ____________________________________________________By completing and submitting this exam, I hereby certify that I have abided by the exam rules and the course Academic Integrity Policy.-114300262254Answers to this exam may be typed into this Word file, or you may print the file, write your answers and then scan the document to .pdf. No other formats will be accepted. The file should be saved as “lastname exam 3”. The completed exam must be submitted to the D2L dropbox by 11:59 pm EDT on Thursday, December 12, 2019. Late papers will not be accepted and result in a grade of 0.The exam is to be completed independently. Only the following resources may be used: the textbook and assigned readings and other course materials linked directly through the course D2L shell or the course CengageNOW page; Microsoft Excel, Excel QM and Excel help files. Any questions about the exam must be posted in the “Exam 3” discussion board on D2L.Good luck!Answers to this exam may be typed into this Word file, or you may print the file, write your answers and then scan the document to .pdf. No other formats will be accepted. The file should be saved as “lastname exam 3”. The completed exam must be submitted to the D2L dropbox by 11:59 pm EDT on Thursday, December 12, 2019. Late papers will not be accepted and result in a grade of 0.The exam is to be completed independently. Only the following resources may be used: the textbook and assigned readings and other course materials linked directly through the course D2L shell or the course CengageNOW page; Microsoft Excel, Excel QM and Excel help files. Any questions about the exam must be posted in the “Exam 3” discussion board on D2L.Good luck!Submit answers to the following questions along with associated output from Excel, Excel QM, or QM for Windows. Include all important work and calculations for all problems for full credit.Consider the tasks, durations, and predecessor relationships in the following CPM network (10 points)ActivityImmediatePredecessors) Duration(Weeks)A---5BA3CB7DB2EA, D6FD4GE2HF5IH, G4JC, I2(a) Draw the project network diagram, with early and late start/finish times.(b) What is the duration of the project?(b) What is the critical path? Consider the following project activities, predecessor activities, and completion times (20 points):ActivityImmediatePredecessors)Optimistic(Weeks)Most Likely(Weeks)Pessimistic(Weeks)1---571021482031712164212353, 46822632347622286781095, 7, 84812109123Draw the project network for this pute the expected duration and variance of each activity. Find the Critical PathWhat is the expected duration and variance of the critical path?What is the probability that the project takes less than 43 weeks?3. Suppose you are concerned about having enough money in your bank account to cover expenses. You earn money as an assistant manager but also have some unpredictable income from selling crafts on Etsy. Your weekly expenses also vary in a probabilistic fashion. The probabilities associated with income and spending are given below (15 points).Weekly incomeProbability?Weekly ExpensesProbability4000.3?3000.14500.4?4000.455000.2?5000.35250.1?6000.15Suppose you begin with $750 in your checking account. Simulate your account balance for the next year (52 weeks), using excel to generate random numbers. Discuss your financial outlook based on the simulation – including descriptive statistics like the max balance, min balance, average balance and standard deviation of the balance.Suppose you will only feel comfortable if have at least $500 in your checking account at the end of the week after all expenses are paid. Based on the simulation results, what is the probability that you will be uncomfortable in any given week?4. Mouse Parts produces mouse ears, white gloves and other parts that are incorporated into the production of Mickey Mouse souvenirs. One of the components used in production has an annual demand of 2500 units, and this is constant throughout the year. Carrying cost is estimated to be $1 per unit per year, and ordering cost is $20 per order (15 points).If the cost of the part is $5, what is the economic order quantity?If there are 300 days of operation per year, and the lead time for an order is 10 days, what is the reorder point?If the lead time for the part is 25 days, what is the reorder point?What is the on-hand reorder point for part (c) if the reorder point is expressed in terms of inventory on hand rather than the inventory position?5. Suppose you operate a car wash, with cars arriving randomly at a rate of .2 customers per minute. Assume that the service times for the car wash follow an exponential distribution with a service time rate of .3 customers per minute. Based on this information, determine each of the following (15 points):a). The probability that no one is at the car wash.b). The average number of customers waitingc). The average number of customers at the car wash altogetherd). The average time a car spends waitinge). The average time a car spends at the car wash altogetherf). The probability a car will have to wait to get their car washed ................
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