Business Mathematics IProject 2: Queuing ProjectGuidelinesSetting: You are working for the People’s Bank. Currently, you have 1 ATM machine that is open 24 hours a day, 7 days a week. The bank manager is currently considering an advertising campaign for 6 service claims. To meet these advertising claims, the bank manager is considering opening up to 3 ATMs in a standard queuingmodel or 3 ATMs with serpentine queuing model. The six service claims are as follows:- Mean Wait Claim: the mean wait time does not exceed a certain value - Maximum Wait Claim: no customer will wait more than a certain value- Percent Delayed: At most a certain percentage of customers will be delayed (wait more than 5 minutes)- Mean Queue Claim: the mean number of people in the line will not exceed a certain value- Percent Irritated Claim: At most a certain percentage of customers will be irritated (number in queue > 3)- Maximum Present Claim: The total number of people present will never exceed a certain valueThe bank manager has determined that the advertising claims will be applicable only to the 9:00am and 9:00pm hours for Friday. To help the bank manager determine the level of service necessary to meet these service claims, the manager has kept 5 weeks worth of records for the arrivals times of customers for each of the two hours. Additionally, the manager has kept records for the service times of the customers for the first week. For our purposes, it will be assumed that the week 1 service times are a representative sample of all services times.In addition to the six advertising claims, the bank manager is considering a gift certificate program for customers who are delayed in the 3 ATM serpentine queuing model. The plan is to reimburse customers with a small monetary reward if they are delayed. To ensure accuracy in this program, the manger is considering upgrading to a stamping system that will record the arrival time of the customer which could then be used to determine how long a customer must wait. The hourly cost for this program will be based on the hourly cost of the gift certificate and the hourly maintenance and operational cost of upgrading to the new system.Using an advanced array of mathematical and computer tools, your team is to determine the level of service necessary to satisfy the six service claims you were given for each of the two hours as well as the hourly cost of the gift certificate program.Below you will find a list of guidelines to assist you in designing and preparing your final report. These guidelines should be treated as such, and should NOT be viewed as a template for designing your presentation. Blindly following the guidelines below will NOT guarantee a high grade on your presentation. Your team’s presentation is to be original in its design and will ultimately be evaluated on its:- Preparedness & Organization- Demonstrated understanding of the problem and the mathematics of the solution- Correct interpretation of the mathematical results as it relates to the project- Demonstrated understanding of the data given to your teamThings to think about as you design your presentation:- Presentation Must be in PowerPoint 8 minutes to discuss your team’s particular findings and final recommendation(s). 5-8 minutes afterwards for questions about the project and your final decision Introduce team members- Team Analysis Define all random variables to be used Show the major steps used in solving the project, but don’t dwell on the minor details. Descriptions of calculations can be left to the written report. IDEALLY your oral report should be a summary of the written report. Major steps of the project include (but are not limited to): Explain the data were given at the beginning of the project and what it all meant. Explain the assumptions in the project Converted histograms of Time Between Arrivals & Service Times into probability densityfunction of continuous random variables Graph of Time Between Arrivals showing exponential distribution Graph for Service Times has unknown distribution Simulations- Explain how and why we bootstrapped with the service times- Explain how and why we used the Monte Carlo method with the time between arrivals- Describe what your simulations were doing. You should be able to explain how we did our simulations in Excel- Summarize the results of all your simulations and explain what it all meant- Explain the level of service that is required to satisfy the six advertising claims- Use your simulations to determine the hourly cost of the gift certificate program- Team Preparedness & Organization Responsibilities and roles are clearly evident and well-defined from presentation The extent to which your team relies on cues from slides or notecards Involvement in the presentation is relevant and equally distributed within team Presentation is well-rehearsed and practiced Ideas and content are presented in a clear and logical order ALL team members are dressed professionally ALL team members are ON TIME and present Presentation is polished, well-organized, and original PowerPoint presentation is used effectively and easy to follow Ability of team members to answer questions posed to them Questions may be posed to individual team members. Once a team member has answered a question, that person cannot answer any further questions. Once all questionshave been asked, any team members may go back and clarify any of the answers that were given to prior questions Questions about mathematical and/or Excel computations should be correctly and clearly explained by any one team member- The following items should be brought with you the day your team makes its final oral report TWO COPIES of your PowerPoint slides 1 copy to turn-in (6 slides per page) 1 copy in case of computer problems (1 slide per page) On a CD you’ll turn in: your PowerPoint file for the presentation your Excel file for the project (it must be easy to read and
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