A fast-food franchise is considering drive-up window food-service operation. It is expected that cars arrival follows a Poisson process with an average inter-arrival time of 3 minutes. Following three...

A fast-food franchise is considering drive-up window food-service operation. It is expected that cars arrival follows a Poisson process with an average inter-arrival time of 3 minutes. Following three alternatives are being considered. Alternative 1: A single channel operation where one employee fills the order and takes the money from the customer. The service time is exponentially distributed with a mean of 2.5 minutes. The employee is paid $9 per hour. Alternative 2: A single channel operation where one employee fills the order and a second employee the takes the money from the customer. The service time is exponentially distributed with a mean of 1.50 minutes. Each employee is paid $9 per hour. Alternative 3: A two channel operation with two service windows, where each window is served by one employee. The service time is exponentially distributed with a mean of 2.5 minutes. The employee at each window is paid $9 per hour. Given that waiting is very costly for a “fast food” business, the franchise attaches a value of $20/hour for each hour of customer waiting in line. Also, to account for equipment and space, an additional cost of $25/hour is attributable to each channel. Fill the table below with your answers. Show the answers to one decimal place accuracy Alt 1 Alt 2 Alt 3 1) Probability that there are no cars in the system - in % 2) Probability that a car must wait for service - in % 3) Average number of cars waiting for service 4) Average number of cars in the system 5) Average time a car waits for service - in minutes 6) Average time spent in the system - in minutes Determine the lowest cost design.