Question

The residents of Bucktown, Illinois, place their trash at the curb each Wednesday morning to be picked up by Municipal Crews. Experience shows 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 group can collect five 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 workday must be collected that evening by an outside contractor who charges $650 per ton. How many crews should the city assigned to trash collection? Treat the number of Crews as a continuous variable.

Answer 1

Answer: 8.56crews

Explanation:

To get critical fractile probability SL,

We stock up the local trash collection capacity.Cost of overstocking by 1 ton =MC = 625/5 = $125Cost of understocking by 1 ton = additional cost of using outside trash pick up = MB = $650-$125 = $5

SL = Prob(RQ) = MB /( MB + MC) = 525/(125 + 525) = 0.8077 appropriate # of crews = 8.56 crews