Only e) and f) please!

A company that operates fast food hamburger restaurant is evaluating the service at its facility. The customers have been observed to arrive at the drive-through window according at an average rate of 30 customers per hour. The restaurant believes the arrival rate conforms to a Poisson distribution. Evaluating the current service rate, the restaurant calculates that the drive-through is capable of processing 40 customers per hour. a. Assuming the service rate is exponentially distributed, what is the utilization rate? b. Evaluate the average time customers spend at the drive-through (time spent in the system). c. The average time spent at drive-throughs for most restaurants is about 4.5 minutes. The company wants to improve on this performance. What complicates the calculation is that the company believes that if drive-through wait times are improved, the restaurant will be more popular. The company therefore has set a target of an average time spent in system of 4 minutes for an arrival rate of 50 customers per hour. What service rate is needed for this level of performance? d. A vendor of specialized drive-through systems has 3 installations available. System A promises a service rate of 60 customers per hour, system B is more expensive but can pro- cess 75 customers per hour and system C' requires a sizable investment and will be capable of processing 90 customers per hour. Which system should the restaurant implement? e. The current facility limits the number of cars (customers) that can be in the drive-through to 5. More than 5 cars in line means customers have to wait on a public street, causing them to leave the restaurant. The restaurant wants to limit the chances of customers balking to less than 5%. How does this information affect the choice made in part (d)? f. The cost of any of the vendor systems is large enough that it is possible to install a second drive-through system for a comparable cost. If a second drive-through is installed, it will be identical to the existing system and have the same performance (40 customers/hour). Can the two requirements (average time-in-system to 4 minutes or less and the probability of more than 5 cars waiting to less than 5%) be met by the two systems if the customer arrival rate increases to 50 customers/hour