Question: Problem #2 (a=5, b=5, total=10 points) Consider a warehouse that uses a fleet of 6 battery-powered automated guided vehicles (AGVs) for material handling. Due to

Problem #2 (a=5, b=5, total=10 points) Consider a

Problem #2 (a=5, b=5, total=10 points) Consider a warehouse that uses a fleet of 6 battery-powered automated guided vehicles (AGVs) for material handling. Due to the wide variety of demands placed on the AGVs, the life of a battery (before a recharging) is a random variable. Suppose the time from recharging a battery for an AGV until it requires recharging again is exponentially distributed with 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 mean of 2 hours. There are two battery-recharging stations, and the distribution centre operates 24 hours per day and 7 days per week. a) Determine the probability of at least one battery recharging station being idle. b) Determine the average number of AGVs waiting to be recharged

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