Waiting Time Question (30 points) Since you last visited the car wash, much has changed. The car wash has simplified its body washing process to do the wheel cleaning automatically, so it is eliminated as a separate step. The car wash also combines washing and waxing into one single step performed by a single automatic machine. The variations in processing times come from the difference between SUVs and regular cars. 14 0 4 Avg. Process Time Process Time Stdev Service (mins) (mins) Resource Used Wash + 1 dedicated automatic Wax machine Interior Cleaning 24 1 dedicated employee Assume customers arrive to the car wash at the rate of 40 cars per day, and that 70% buy Basic (which only includes wash + wax), and the remaining 30% buy the Premium package (which includes wash, wax, and interior cleaning). The car wash operates for 12 hours each day. Assume inter-arrival times to each service are exponentially distributed. a) (8 points) What is the average wait time for Wash+Wax step in minutes? Avg. Wait Time for Wash+Wax = mins. b) (7 points) What is the avg. throughput time for Interior Cleaning in minutes to the closest number? Avg. TPT for Interior Cleaning = mins. c) (4 points) What is the avg. throughput time for Premium customers through the car wash in minutes to the closest number? Avg. TPT for Premium Customers = mins. d) (4 points) What is the avg. TPT for an average customer with one vehicle through the car wash? a) (8 points) What is the average wait time for Wash+Wax step in minutes? Avg. Wait Time for Wash+Wax = mins. b) (7 points) What is the avg. throughput time for Interior Cleaning in minutes to the closest number? Avg. TPT for Interior Cleaning = mins. c) (4 points) What is the avg. throughput time for Premium customers through the car wash in minutes to the closest number? Avg. TPT for Premium Customers = mins. d) (4 points) What is the avg. TPT for an average customer with one vehicle through the car wash? Avg. TPT for an average customer mins. e) (7 points) The average number of customers waiting at any step in the car wash is: Avg. No. of Cars Waiting = cars Waiting Time Question (30 points) Since you last visited the car wash, much has changed. The car wash has simplified its body washing process to do the wheel cleaning automatically, so it is eliminated as a separate step. The car wash also combines washing and waxing into one single step performed by a single automatic machine. The variations in processing times come from the difference between SUVs and regular cars. 14 0 4 Avg. Process Time Process Time Stdev Service (mins) (mins) Resource Used Wash + 1 dedicated automatic Wax machine Interior Cleaning 24 1 dedicated employee Assume customers arrive to the car wash at the rate of 40 cars per day, and that 70% buy Basic (which only includes wash + wax), and the remaining 30% buy the Premium package (which includes wash, wax, and interior cleaning). The car wash operates for 12 hours each day. Assume inter-arrival times to each service are exponentially distributed. a) (8 points) What is the average wait time for Wash+Wax step in minutes? Avg. Wait Time for Wash+Wax = mins. b) (7 points) What is the avg. throughput time for Interior Cleaning in minutes to the closest number? Avg. TPT for Interior Cleaning = mins. c) (4 points) What is the avg. throughput time for Premium customers through the car wash in minutes to the closest number? Avg. TPT for Premium Customers = mins. d) (4 points) What is the avg. TPT for an average customer with one vehicle through the car wash? a) (8 points) What is the average wait time for Wash+Wax step in minutes? Avg. Wait Time for Wash+Wax = mins. b) (7 points) What is the avg. throughput time for Interior Cleaning in minutes to the closest number? Avg. TPT for Interior Cleaning = mins. c) (4 points) What is the avg. throughput time for Premium customers through the car wash in minutes to the closest number? Avg. TPT for Premium Customers = mins. d) (4 points) What is the avg. TPT for an average customer with one vehicle through the car wash? Avg. TPT for an average customer mins. e) (7 points) The average number of customers waiting at any step in the car wash is: Avg. No. of Cars Waiting = cars