Problem 5: In an effort to better understand its customers' needs, Magic Suds Car Wash has collected data regarding customer arrivals and service capacity. In a typical day, customers arrivals range between 4 and 7 per hour. Magic Suds is capable of serving 5 to 8 customers per hour. Customers are served on a first-come, first-served basis. Probability distributions for customer arrivals and service capacity are shown in the tables below. Using Excel, the car wash process was simulated for a period of 10 hours; the results are reported below. The random numbers for the simulation (labeled as RN1 and RN2) were generated using the function, RANDO 1 Magic Suds Car Wash Simulation 3 Probability Distribution for Number of Arrivals per hour bability Distribution for Number of Customers Served per hour Number of Arrivals, x Number Lower U 0.00 0.20 0.45 0.70 0.20 0.40 0.30 0.10 0.00 0.20 0.60 0.90 0.20 0.25 0.25 0.30 0.20 0.45 0.70 1.00 0.20 10 11 Simulation Replications Possibly Actually Served Served Customer Total to be RN2 12 Hour Waiting RN1 13 14 15 0 0.4455 0 0.5460 0 0.5303 0 0.5313 0 0.5582 0 0.6780 0.0601 0 0.7883 0 0.7921 0 0.8627 5 0.3228 6 0.7059 6 0.5614 6 0.7262 6 0.6307 0.0005 5 0.9503 7 0.6633 7 0.8691 7 0.1497 17 18 19 20 21 6 10 a). Why would the service rate vary? Identify at least two (2) reasons why the rate at which customers are served would fluctuate. [2 pts]. b). For hour 7 above (row 19), very briefly indicate how the numbers in each column were computed or derived. You may write a formula or a few words for each item. [2 pts each] 12 13 Hour Waiting Arrivals Served Served served 5 0.3228 6 0.7059 6 0.5614 6 0.7262 6 0.6307 6 0.0005 5 0.9503 7 0.6633 7 0.8691 7 0.1497 0 0.4455 0 0.5460 0 0.5303 00.5313 0 0.5582 0 0.6780 10.0601 0 0.7883 0 0.7921 0 0.8627 15 16 17 18 6 6 6 20 21 10 a). Why would the service rate vary? Identify at least two (2) reasons why the rate at which customers are served would fluctuate. [2 pts] b). For hour 7 above (row 19), very briefly indicate how the numbers in each column were computed or derived. You may write a formula or a few words for each item. [2 pts each] Waiting (column B) Customer Arrivals (column D) Possibly Served (column G) Actually Served (column H) c). What is the average number of customers waiting to be served? (Be sure to show work/explain reasoning.) [4 pts] d). What is the average number of customers actually served? (Be sure to show work/explain reasoning.) [4 pts e). Jorge Martinez, the manager of Magic Suds, is skeptical of the numbers computed above in parts c and d. List two (2) reasons why Martinez's skepticism is justified. [2 pts] Problem 5: In an effort to better understand its customers' needs, Magic Suds Car Wash has collected data regarding customer arrivals and service capacity. In a typical day, customers arrivals range between 4 and 7 per hour. Magic Suds is capable of serving 5 to 8 customers per hour. Customers are served on a first-come, first-served basis. Probability distributions for customer arrivals and service capacity are shown in the tables below. Using Excel, the car wash process was simulated for a period of 10 hours; the results are reported below. The random numbers for the simulation (labeled as RN1 and RN2) were generated using the function, RANDO 1 Magic Suds Car Wash Simulation 3 Probability Distribution for Number of Arrivals per hour bability Distribution for Number of Customers Served per hour Number of Arrivals, x Number Lower U 0.00 0.20 0.45 0.70 0.20 0.40 0.30 0.10 0.00 0.20 0.60 0.90 0.20 0.25 0.25 0.30 0.20 0.45 0.70 1.00 0.20 10 11 Simulation Replications Possibly Actually Served Served Customer Total to be RN2 12 Hour Waiting RN1 13 14 15 0 0.4455 0 0.5460 0 0.5303 0 0.5313 0 0.5582 0 0.6780 0.0601 0 0.7883 0 0.7921 0 0.8627 5 0.3228 6 0.7059 6 0.5614 6 0.7262 6 0.6307 0.0005 5 0.9503 7 0.6633 7 0.8691 7 0.1497 17 18 19 20 21 6 10 a). Why would the service rate vary? Identify at least two (2) reasons why the rate at which customers are served would fluctuate. [2 pts]. b). For hour 7 above (row 19), very briefly indicate how the numbers in each column were computed or derived. You may write a formula or a few words for each item. [2 pts each] 12 13 Hour Waiting Arrivals Served Served served 5 0.3228 6 0.7059 6 0.5614 6 0.7262 6 0.6307 6 0.0005 5 0.9503 7 0.6633 7 0.8691 7 0.1497 0 0.4455 0 0.5460 0 0.5303 00.5313 0 0.5582 0 0.6780 10.0601 0 0.7883 0 0.7921 0 0.8627 15 16 17 18 6 6 6 20 21 10 a). Why would the service rate vary? Identify at least two (2) reasons why the rate at which customers are served would fluctuate. [2 pts] b). For hour 7 above (row 19), very briefly indicate how the numbers in each column were computed or derived. You may write a formula or a few words for each item. [2 pts each] Waiting (column B) Customer Arrivals (column D) Possibly Served (column G) Actually Served (column H) c). What is the average number of customers waiting to be served? (Be sure to show work/explain reasoning.) [4 pts] d). What is the average number of customers actually served? (Be sure to show work/explain reasoning.) [4 pts e). Jorge Martinez, the manager of Magic Suds, is skeptical of the numbers computed above in parts c and d. List two (2) reasons why Martinez's skepticism is justified. [2 pts]
