1. A receiving operator for a large grocery store is analyzing her operations. Trucks arrive to the loading dock at an average rate of four per hour for 8 hours each day. The cost of operating a truck is estimated to be $80 per hour. Trucks are met by a three-person crew, which is able to unload the truck in an average of 12 minutes. The payroll associated with each crew member is $22/hour. It is possible to install new equipment to help the crew operate more efficiently, decreasing the unloading time from 12 minutes to 9 minutes per truck. There is an additional cost for this equipment that is estimated to be $500/day. Should the new equipment be installed? a) Consider the performance of the crew before the new equipment is installed. On average, how many trucks are in the system (to the nearest 0.1 trucks) given the arrival and service rates? b) Consider the performance of the crew before the new equipment is installed. On average, how many hours (to the nearest 0.1 hours) does each truck spend in the system given the arrival and service rates? c) Consider the performance of the crew before the new equipment is installed. Based on the average number of trucks in the system, what is the total system cost (to the nearest dollar) per day (crew cost and truck cost)? d) Consider the performance of the crew after the new equipment is installed. On average, how many trucks (to the nearest 0.1 trucks) are in the system given the arrival and the new service rate? e) Consider the performance of the crew after the new equipment is installed. On average, how many hours (to the nearest 0.1 hours) does each truck spend in the system given the arrival and the new service rate? f) Consider the performance of the crew after the new equipment is installed. Based on the average number of trucks in the system, what is the total system cost (to the nearest dollar) per day (crew cost and truck cost)? g) Based on your cost analysis - is it worth it to install the new equipment? 2. A chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every two minutes. The average request require 1.7 minutes to fill. Maintenance employees are paid $20 per hour and warehouse employees are paid $12 per hour. The warehouse operates 8 hours per day. a) Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day (to the nearest $) if there is only 1 warehouse employees working? b) Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day (to the nearest $) if there are 2 warehouse employees working? c) Based on the number of maintenance employees in the system, an 8 hour work day, and the given arrival and service rates. What is the system cost per day (to the nearest $) if there are 3 warehouse employees working? d) What is the optimal number of warehouse employees to staff the warehouse? 3. A computer processes jobs on a first-come, first-served basis. The jobs arrive to the computer every 6 minutes. The objective in processing these jobs is that they spend no more than eight minutes, on average, in the system. (Hint: you can use the Goal Seek function to help with part b) a) What is the arrival rate (in jobs/hour)? b) What is the speed that computer must be a have to process jobs, on average (in jobs/hour), to meet this objective (enter to nearest 0.1 job/hour)? Obviously, processing a million jobs per hour would meet the objective - what I want to know is the slowest processing speed that meets this objective