Note: For all these problems assume Poisson arrivals and exponential service time

MBJ A receiving operator for a large grocery store is analyzing her operations. Trucks arrive to the loading clock at an average rate of four per hour for each day. The cost of operating a truck is estimated to be $75 per hour. Trucks are met by a two-person crew, the crew can unload the truck in an average of 9 minutes. The payroll associated with each crew member is $18/hour. It is possible to install new equipment to help the crew operate more efciently, decreasing the unloading time from 9 minutes to 7 minutes per truck. Rental of this equipment would increase the daily cost of the operation by $200 per day. Assume each day is an 8-hour shift. Should the new equipment be installed? a) b) d) 1') cl Consider the performance of the crew before the new equipment is installed. On average, how many trucks are in the system (to the nearest 0.01 trucks) given the arrival and service rates? Consider the performance of the crew before the new equipment is installed. On average, how many hours (to the nearest 0.01 hours) does each truck spend in the system given the arrival and service rates? Consider the performance of the crew before the new equipment is installed. Basing your cost on the number of trucks in the system, what is the total system cost (to the nearest dollar) w d_ay (crew cost and truck cost)? Consider the performance of the crew m the new equipment is installed. On average, how many trucks (to the nearest 0.01 trucks) are in the system given the arrival and the new service rate? Consider the performance of the crew after the new equipment is installed. On average, how many hours (to the nearest 0.01 hours) does each truck spend in the system given the arrival and the new service rate? Consider the performance of the crew after the new equipment is installed. Basing your cost on the number of trucks in the system, what is the total system cost (to the nearest dollar) per day (crew cost and truck cost)? Based on your cost analysis - is it worth it to install the new equipment? M82 Cullowhee Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Cullowhee's management would like to evaluate the following two alternatives: 0 Option 1: Provide extra training to the existing consultant which will result in average service time of 8 minutes per customer. 0 Option 2: Hire an additional consultant, each consultant would have an average service time per customer of 10 minutes. The consultants are paid $16 per hour and the customer waiting time is valued at $25 per hour for waiting time prior to service. a) What is hourly system cost for the system with one consultant (Option 1 - two decimal places)? b) What is hourly system cost for the system with two consultants (Option 2 - two decimal places)? c) Should Cullowhee expand to the two-consultant system