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Business Mathematics IHomework 10Solution.Solution.Business Mathematics IHomework 10Prepared forStephen ReyesMath 115a, Section University of Arizona ByTeam #Submitted onDateWe, the undersigned, affirm that all of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we understand that sanctions will be imposed individually as well as jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature1. (Exercise 1 from Monte Carlo Methods) Go to Excel and use RAND to create a column of 12 random numbers, between 0 and 1.Solution. 2. (Exercise 3 from Monte Carlo Methods) Add a column to the file If.xls that simulates 10 tosses of a coin that is loaded in such a way that you are three times as likely to get a tail as a head. Show the formula that you used in the column.Solution. 3. (Exercise 8 from Monte Carlo Methods) Recall the tractor company that we studied in Examples 2 and 4 of the section Bayes’ Theorem in Project 1. All of their vehicles are produced on one of the three assembly lines, Red, White, or Blue. The Excel file Tractors.xls simulates the company’s production of 10,000 tractors. Open that file and look at the formulas in Cells B14:D14 to see how RAND and IF functions are used in the simulation. (i) Modify Tractors.xls to reflect the company’s production, assuming that 35% of the company’s tractors are made on the Red line and 25% are made on the Blue line. (ii) Use the modified file to estimate the fraction of non-starting tractors that the company will produce.Solution. 4. (Exercise 12 from Monte Carlo Methods) Modify the Excel file Queuing Example 2.xls, so that it will create, and correctly plot, random samples of size 500 for an exponential random variable, X, with parameter 10.Solution. 5. (Exercise 15 from Monte Carlo Methods) Create new worksheets or modify the worksheets in Queue Focus.xls to accommodate the maximum number of arrivals that is indicated in your team assignment. Note that the allowable maximum number of arrivals in worksheetsof Queue Focus.xls cannot be extended by simply dragging down existing rows. For example, the entries in Column L of 1 ATM depend on criteria ranges that contain two rows. After these cells are dragged down, they will need to be adjusted with individual typing. The necessary extensions of criteria ranges will also require careful thought. In addition, you willneed to adjust the ranges of rows that are considered in all summary cells as well as the Overflow cutoffs. Solution.6. (Exercise 16 from Monte Carlo Methods) Modify your team data worksheets so that all simulations kept track of the numbers of customers who are irritated.Solution. 7. (Exercise 17 from Monte Carlo Methods) (i) Collect summary data from at least 2,000 simulations for each of 1 ATM, 2 ATM’s, 3 ATM’s, and 3 ATM’s with serpentine queue during your team’s first hour. (ii) Repeat Part (i) for your team’s second hour. Solution. 8. (Exercise 18 from Monte Carlo Methods) (i) Create tables, similar to those in the Focus on the Project Section, that display the numbers of ATM’s and (in the case of 3 ATM’s) the type of queues that would be needed to validate each of your team’s possible advertising claims during your team’s first hour. (ii) Repeat Part (i) for your second hour.


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UA MATH 115A - Homework

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