A two$-$server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is $2$ minutes for each server.

a$.$ What is the probability that there are no cars in the system?

b$.$ What is the average number of cars waiting for service?

c$.$ What is the average number of cars in the system?

d$.$ What is the average time a car waits for service?

e$.$ What is the average time in the system?

f$.$ What is the probability that an arriving car will have to wait for service?

g$.$ What is your recommended design option?

h$.$ The following cost information is available for the fastfood franchise:

i$.$ Customer waiting time is valued at $$25$ per hour to reflect the fact that waiting time is costly for the fast$-$food business.

ii$.$ The cost of each employee is $$6\mathrm{.}50$ per hour.

iii. To account for equipment and space, an additional cost of $$20$ per hour is attributable to each channel.

What is the lowest cost design for the fast$-$food business?