A receiving operator for a large grocery store is analyzing her operations. Trucks arrive to the loading dock at an average rate of three per hour for each day. The cost of operating a truck is estimated to be $90 per hour. Trucks are met by a three-person crew, the crew can unload the truck in an average of 15 minutes. The payroll associated with each crew member is $28/hour. It is possible to install new equipment to help the crew operate more efficiently, decreasing the unloading time from 15 minutes to 12 minutes per truck. There is an additional cost for this equipment that is estimated to be $250/day. Assume each day is an 8-hour shift. 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?