Henry Clements is a friend of yours who has a car rental agency in major metropolitanarea. Although he is an independent company he works closely with three other independentcompanies in metro area. They share information and each they forecast the number of cars eachwill need the following week. Then if needed, the will transfer cars between location on Sundaywhen none of the agencies is open. If they have to go and get a car during the week, it will cost$75 each considering the lost time and good will of making the customer wait. Moving onSunday gives the customer the option to return the car to any of the four locations and it hasallowed Henry and the other agencies access to extra cars to meet their needs. Everyone ishappy with this arrangement.Henry reviewed his companys performance and he believes there is room forimprovement. He has obtain records for the last three months. The data he collected are shownbelow. It is Friday and he has to input his forecast for the number of cars needed tomorrow. Heknows you are have been taking a class in Quantitative Analysis and has asked you to review hisdata and help with his forecast and determine what else he might to do increase his performance.As you discuss the situation with him, you learn that he wants to be able to meet the customersrequirement for a vehicle 95% of the time. He says he rarely ever gets complaints if the exactmodel is not available, as long as he has a vehicle available, so he does not try to anticipateparticular size or model requests and lets randomness take care of that. Weekly demand is asfollows.Week 1 126 Week 7 243Week 2 200 Week 8 167Week 3 243 Week 9 131Week 4 167 Week 10 208Week 5 132 Week 11 251Week 6 211 Week 12 171In the past Henry has used the average number of cars as his basic number and adjustedto meet his goal of 95% service. He asks you about some other methods he has heard about.1. What should his forecast be using his method? What are the mean and standard deviationof the demand?2. What would the forecast be if he used regression analysis? What is the regressionformula? What is the r value?3. What about time-series forecasting? There are at least six time-series methods. Which isbest? What is the MAD of each option?4. What will you tell him about which is the best option?Henry has two people who can check cars out for a rental. One works at the servicecounter and the other works in the office and can come out to help if needed. Henry hasdetermined that people arrive following a Poisson distribution. Rentals average about 24 per dayand the service person take about 15 minutes to process a customer for a rental. [Note. Henrysbusiness is in a community, not in an airport, so he is only open 8 hours a day.] Henry sees thatthe agent at the service counter in not busy all the time so he is contemplating not keeping theoffice person trained and leaving only the service counter person.5. Is this a wise move? What is the average time the customer takes from when he/shearrives until he/she has a car?6. Currently, when the office person in serving customers, a second line forms in front ofthe counter. Is that how Henry should set up the waiting area or is there a better way?7. What are the time in the queue and time in the system for your proposed method (ifdifferent from Question 2.When a car is returned to his location, Henry has three employees who prepare the car forthe next rental. As a car arrives, one of the employees takes the car and washes it, cleans andvacuums it, and inspects it and prepares the paperwork for the next rental and returns the car tothe lot. The employees each take a car in sequence. Henry has observed the process and hasobserved the time each takes to complete each step. He asks you if there is a better way toorganize this part of the operations. The information about the times (in minutes) is as follow:Wash Vacuum Inspect & returnBeverly 22 13 11Cameron 15 17 20Tina 19 19 14Each rental requires two agreement forms, one for when the car is checked out and onewhen it is checked in. Henry orders these form from a local printer. The printer charges Henry$40 to set up the printer. The forms cost 50 cents each. Because of the damage to the forms andthe forms becoming obsolete, it cost Henry 25% to store the forms. The printer will only acceptorders in multiples of 100.8. If the three months of data collected and presented above is indicative of all demand, howmany forms should Henry order?9. The printer offers Henry a 10% discount if Henry orders 5000 or more form at a time.Would this be advantageous to Henry?10. How much would it save if any?Henry is now ready compute what do with the cars on Sunday. The other locations reportthe following on-hand and needed cars. Henry will have 150 cars on-hand Saturday night.Location North Location East Location SouthOn-hand 165 180 210Needed 195 160 190Based on past experience, the cost to move cars is:Between And CostHenry Location North $12Henry Location East $22Henry Location South $17Location North Location East $7Location North Location South $28Location East Location South $1411. How many cars will need to be moved and what will the total cost of the move be?12. Based on all the above computations, what would you recommend to Henry about hisoperation and what changes would you propose (if any)?Henry Clements is a friend of yours who has a car rental agency in major metropolitanarea. Although he is an independent company he works closely with three other independentcompanies in metro area. They share information and each they forecast the number of cars eachwill need the following week. Then if needed, the will transfer cars between location on Sundaywhen none of the agencies is open. If they have to go and get a car during the week, it will cost$75 each considering the lost time and good will of making the customer wait. Moving onSunday gives the customer the option to return the car to any of the four locations and it hasallowed Henry and the other agencies access to extra cars to meet their needs. Everyone ishappy with this arrangement.Henry reviewed his companys performance and he believes there is room forimprovement. He has obtain records for the last three months. The data he collected are shownbelow. It is Friday and he has to input his forecast for the number of cars needed tomorrow. Heknows you are have been taking a class in Quantitative Analysis and has asked you to review hisdata and help with his forecast and determine what else he might to do increase his performance.As you discuss the situation with him, you learn that he wants to be able to meet the customersrequirement for a vehicle 95% of the time. He says he rarely ever gets complaints if the exactmodel is not available, as long as he has a vehicle available, so he does not try to anticipateparticular size or model requests and lets randomness take care of that. Weekly demand is asfollows.Week 1 126 Week 7 243Week 2 200 Week 8 167Week 3 243 Week 9 131Week 4 167 Week 10 208Week 5 132 Week 11 251Week 6 211 Week 12 171In the past Henry has used the average number of cars as his basic number and adjustedto meet his goal of 95% service. He asks you about some other methods he has heard about.1. What should his forecast be using his method? What are the mean and standard deviationof the demand?2. What would the forecast be if he used regression analysis? What is the regressionformula? What is the r value?3. What about time-series forecasting? There are at least six time-series methods. Which isbest? What is the MAD of each option?4. What will you tell him about which is the best option?Henry has two people who can check cars out for a rental. One works at the servicecounter and the other works in the office and can come out to help if needed. Henry hasdetermined that people arrive following a Poisson distribution. Rentals average about 24 per dayand the service person take about 15 minutes to process a customer for a rental. [Note. Henrysbusiness is in a community, not in an airport, so he is only open 8 hours a day.] Henry sees thatthe agent at the service counter in not busy all the time so he is contemplating not keeping theoffice person trained and leaving only the service counter person.5. Is this a wise move? What is the average time the customer takes from when he/shearrives until he/she has a car?6. Currently, when the office person in serving customers, a second line forms in front ofthe counter. Is that how Henry should set up the waiting area or is there a better way?7. What are the time in the queue and time in the system for your proposed method (ifdifferent from Question 2.When a car is returned to his location, Henry has three employees who prepare the car forthe next rental. As a car arrives, one of the employees takes the car and washes it, cleans andvacuums it, and inspects it and prepares the paperwork for the next rental and returns the car tothe lot. The employees each take a car in sequence. Henry has observed the process and hasobserved the time each takes to complete each step. He asks you if there is a better way toorganize this part of the operations. The information about the times (in minutes) is as follow:Wash Vacuum Inspect & returnBeverly 22 13 11Cameron 15 17 20Tina 19 19 14Each rental requires two agreement forms, one for when the car is checked out and onewhen it is checked in. Henry orders these form from a local printer. The printer charges Henry$40 to set up the printer. The forms cost 50 cents each. Because of the damage to the forms andthe forms becoming obsolete, it cost Henry 25% to store the forms. The printer will only acceptorders in multiples of 100.8. If the three months of data collected and presented above is indicative of all demand, howmany forms should Henry order?9. The printer offers Henry a 10% discount if Henry orders 5000 or more form at a time.Would this be advantageous to Henry?10. How much would it save if any?Henry is now ready compute what do with the cars on Sunday. The other locations reportthe following on-hand and needed cars. Henry will have 150 cars on-hand Saturday night.Location North Location East Location SouthOn-hand 165 180 210Needed 195 160 190Based on past experience, the cost to move cars is:Between And CostHenry Location North $12Henry Location East $22Henry Location South $17Location North Location East $7Location North Location South $28Location East Location South $1411. How many cars will need to be moved and what will the total cost of the move be?12. Based on all the above computations, what would you recommend to Henry about hisoperation and what changes would you propose (if any)?