The city of Dilworth spends $$100,000$ a year on janitorial services for city buildings. Rather than set up a separate funding source for janitorial services, the city would prefer to pass along the costs to its four departments and its city council as an indirect cost. The city added up the total number of hours worked in a year by its janitors and found it to be $2,080$ hours. The city also found that the number of hours spent by the janitors on the different department offices over the past year were:

Public Safety: $728$ hours

Management: $416$ hours

Streets & Sanitation: $520$ hours

Recreation: $312$ hours

City Council: $104$ hours

What is the cost pool? What is the cost base? What dollar amount in indirect costs should be allocated to each department as well as the city council? Please explain your calculations.