The residents of Bucktown, Illinois, place their trash at the curb each Wednesday morning to be picked up by municipal crews. Experience shows that the total amount of trash put out has a normal distribution with a mean of 35 tons and a standard deviation of 9 tons. Crews of full- time city employees assigned to trash collection collect trash. Each crew can collect 5 tons of trash per working day. The city has plenty of trucks of the kind used for trash collection. The marginal cost of operating one trash collection crew for one working day, including both personnel- related costs and truck- related costs, is reckoned at $ 625. Whatever trash remains at the end of the work day must be collected that evening by an outside contractor who charges $ 650 per ton. How many crews should the city assign to trash collection? For simplicity, treat the number of crews as a continuous variable.
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