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Robot Company franchises combination gas and car wash stations throughout the United States. Robot gives a free car wash for a gasoline fill-up or, for a wash alone, charges $0.50. Past experience shows that the number of customers that have car washes following fill-ups is about the same as for a wash alone. The average profit on a gasoline fill-up is about $0.70, and the cost of the car wash to Robot is $0.10. The robot stays open 14 hours per day.
The robot has three power units and drives assemblies, and a franchisee must select the unit preferred. Unit I can wash cars at the rate of one every five minutes and is leased for $12 per day. Unit II, a larger unit, can wash cars at the rate of one every four minutes but costs $16 per day. Unit III, the largest, costs $22 per day and can wash a car in three minutes.
The franchisee estimates that customers will not wait in line for more than five minutes for a car wash. A longer time will cause Robots to lose gasoline sales as well as the car wash sale.
If the estimate of customer arrivals resulting in washes is 10 per hour, which wash unit should it be selected?
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