The purpose of the assignment is to gather the information needed toset up problems, run simulations, and interpret the results to solvethe problems.

Using specified data files, chapter example files, and templatesfrom the “Topic 2 Student Data, Template, and ExampleFiles” topic material, complete Chapter 15, Problems 2, 7, 9, 32(parts a and b only), 33, and 35 from the textbook. Use the PalisadeDecisionTools Excel software to complete these problems whererequested and applicable. Problem 2 only requires the use of MicrosoftExcel; however, you may optionally use the Palisade DecisionToolsExcel software to generate the histogram.

Use the Palisade DecisionTools Excel software to complete the restof the problems and ensure that all Palisade software output isincluded in your files. Unless otherwise stated, run simulations with1,000 trials. Use 500 trials if the software will not allow you to run1,000 trials. Ensure that only one Excel file is open when running a simulation.

To receive full credit on the assignment, complete the following.

1. Ensure that the Palisade software output is included with yoursubmission.
2. Ensure that Excel files include the associatedcell functions and/or formulas if functions and/or formulas areused.
3. Include a written response to all narrative questionspresented in the problem by placing it in the associated Excelfile.
4. Include screenshots of all simulation distributionresults for output variables.
5. Place each problem in its ownExcel file. Ensure that your first and last name are in your Excelfile names.

APA style is not required, but solid academic writing is expected.

This assignment uses a rubric. Please review the rubric prior tobeginning the assignment to become familiar with the expectations forsuccessful completion. 2.UseExcel’s functions (not @RISK) to generate 1000random numbers from anormal distribution with mean 100 and standard deviation 10. Then freezethese random numbers.a.Calculate the mean and standard deviation ofthese random numbers. Are they approximately what you wouldexpect?b.What fraction of these random numbers are within k standarddeviations of the mean? Answer for kkk=1; for k=2; for k=3. Are theanswers close to what they should be (according to the empirical rulesyou learned in Chapters 2 and 5)?c.Create a histogram of the randomnumbers using 10to 15 categories of your choice. Does this histogramhave approximately the shape you would expect?7.Use@RISK’s Define Distributions tool to draw a triangular distributionwith parameters 200, 300, and 600. Then superimpose a normaldistribution on this drawing, choosing the mean and standard deviationto match those from the triangular distribution. (Click the Add Overlaybutton at the bottom of the window and then choose the distribution tosuperimpose.)a.What are the 5th and 95th percentiles for these twodistributions?b.What is the probability that a random number from thetriangular distribution is less than 400? What is this probability forthe normal distribution?c.Experiment with the sliders to answerquestions similar to those in part b. Would you conclude that these twodistributions differ most in the extremes (right or left) or in themiddle? Explain.9.Acompany is about to develop and then market a new product. It wants tobuild a simulation model for the entire process, and one key uncertaininput is the development cost. For each of the following scenarios,choosean appropriate distribution together with its parameters, justify yourchoice in words, and use @RISK’s Define Distributions tool to show yourcho-sen distribution.a.Company experts have no idea what thedistribution of the development cost is. All they can state is “we are95% sure it will be at least $450,000, and we are 95% sure it will be nomore than $650,000.”b.Company experts can still make the same statementas in part a, but now they can also state: “We believe the distributionis symmetric, reasonably bell-shaped, and its most likely value isabout $550,000.”c.Company experts can still make the same statement asin part a, but now they can also state: “We believe the distribution isskewed to the right, and its most likely value is about $500,000.”32.Ahardware company sells a lot of low-cost, high-volume products. For onesuch product, it is equally likely that annual unit sales will be lowor high. If sales are low (60,000), the company can sell the product for$10 per unit. If sales are high (100,000), a competitor will enter andthe company will be able to sell the product for only $8 per unit. Thevariable cost per unit has a 25% chance of being $6, a 50% chance ofbeing $7.50, and a 25% chance of being $9. Annual fixed costs are$30,000.a.Use simulation to estimate the company’s expected annualprofit.b.Find a 95% interval for the company’s annual profit, that is,an interval such that about 95% of the actual profits are inside it.33.W. L. Brown, a direct marketer of women’s clothing, must determine howmany telephone operators to schedule during each part of the day. W. L.Brown estimates that the number of phone calls received each hour of atypical eight-hour shift can be described by the probabilitydistribution in the file P15_33.xlsx. Each operator can handle 15 callsper hour and costs the company $20 per hour. Each phone call that is nothandled is assumed to cost the company $6 in lost profit. Consideringthe options of employing 6, 8, 10, 12, 14, or 16 operators, usesimulation to determine the number of operators that minimizes theexpected hourly cost (labor costs plus lost profits).35.Lemington’sis trying to determine how many Jean Hudson dresses to order for thespring season. Demand for the dresses is assumed to follow a normaldistribution with mean 400 and standard deviation 100. The contractbetween Jean Hudson and Lemington’s works as follows. At the beginningof the season, Lemington’s reserves x units of capacity. xxLemington’smust take delivery for at least 0.8xdresses and can, if desired, takedelivery on up to xdresses. Each dress sells for $160 and Hudson charges$50 per dress. If Lemington’s does not take delivery on all x dresses,it owes Hudson a $5 penalty for each unit of reserved capacity that isunused. For example, if Lemington’s orders 450 dresses and demand is for400 dresses, Lemington’s will receive 400 dresses and owe Jean400($50)+50($5). How many units of capacity should Lemington’s reserveto maximize its expected profit?AND THESE 2 QUESTIONS… Question 1-

Consider the following scenario and address the questions that follow.

Suppose your company wanted to determine the amount of sales of a new SUV model, called Lightning.The sales estimate would be based on the overall demand of various SUVmodel types. Overall demand is assumed to be normally distributed with amean of 3 million units and standard deviation of 500,000 units. Theshare of demand that Lightning will take is assumed to be 4%.After running 1,000 simulated scenarios, a 95% confidence interval wasconstructed for the expected sales of Lightning units sold with limits of 93,048 and 146,964.

1. If 1,000 new simulated scenarios were run, would you get the exact result? Explain why.
2. Would the results be more stable if you ran 2,000 runs? Explain why.
3. Is there a number of simulations that can be run so that the results do not change if you re-ran the simulations? Explain. QUESTION 2-
   Reconsider the scenario presented in DQ 1 and address the questions that follow.Suppose your company wanted to determine the amount of sales of a new SUV model, called Lightning.The sales estimate would be based on the overall demand of various SUVmodel types. Overall demand is assumed to be normally distributed with amean of 3 million units and standard deviation of 500,000 units. Theshare of demand that Lightning will take is assumed to be 4%.After running 1,000 simulated scenarios, a 95% confidence interval wasconstructed for the expected sales of Lightning units sold with limits of 93,048 and 146,964.

   1. If a mean of 6 million units was used in the simulation, how would the confidence interval change? Explain.
   2. How would the confidence interval change if a standard deviation of 250,000 was used? Explain.