Business Mathematics I Homework 10 Prepared for Stephen Reyes Math 115a, Section University of Arizona By Team # Submitted on Date We, 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) ______________________________ ______________________________ Name (typed) ______________________________ ______________________________ Name (typed) ______________________________ ______________________________ Name (typed) Signature Signature Signature Signature ______________________________ ______________________________ Name (typed) Signature 1. (Exercise 1 from <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) Go to Excel and use RAND to create a column of 12 random numbers, between 0 and 1. Solution. 2. (Exercise 3 from <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) 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 <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) 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 <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) 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 <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) 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 worksheets of 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 will need to adjust the ranges of rows that are considered in all summary cells as well as the Overflow cutoffs. Solution. 6. (Exercise 16 from <a href="/keyword/monte-carlo-methods/" ><a href="/keyword/monte-carlo-method/" ><a href="/keyword/monte-carlo/" >monte carlo</a> method</a> s</a> ) Modify your team data worksheets so that all simulations ...