A vanilla milkshake machine requires a constant 3 minutes to make the special shake served at the Burger Shack. The machine can process one vanilla shake at a time. Requests for the special shake occur every 4 minutes, or 15 per hour on average. Compute the following:
a. Probability that the shake machine is busy
b. Probability that the shake machine is not busy
c. Average amount of time spent waiting to use the shake machine
d. Average amount of time spent in the shake process (waiting and processing time)
e. Average number of shakes ordered but not yet started processing (i.e., waiting for machine)
f. Average number of shakes in process (ordered but not yet delivered to customers)