Consider a distribution center that uses a fleet of eight battery-powered automated guided vehicles for material delivery. Due to the wide variety of demands placed on an AGV, the life of a battery, before recharging is required, is a random variable. Suppose the time from recharging a battery for an AGV until it requires recharging again is exponentially distributed with a mean value of 10 hours. Also, suppose the AGV is idle during battery recharging. Finally, suppose the time required to recharge a battery is also exponentially distributed with a mean of 2 hours. There are two battery recharging machines, and the distribution center operates 24 hours a day and 7 days a week.

a. Determine the probability of at least one battery recharging machine being idle.

b. Determine the average number of AGVs waiting to be recharged. (Don’t include those being recharged.)