Data collected at a parking lot indicate that a total of $250$ ?cars park between $9$ ?a$.$m$.$ ?and

$5$ ?p$.$m$.5\%$ ?of these cars are parked for an average of $2$ ?hr$,20\%$ ?for an average of $3$ ?hr$,10\%$ ?for an average of $4$ ?hr$,$ ?and the remaining cars are parked for an average of $8$ ?hr$.$

a$.$ ?Determine the space$-$hours of demand at the lot.

b$.$ ?If $10\%$ ?of the parking bays are vacant on average $($between $9$ ?a$.$m$.$ ?and $5$ ?p$.$m$.)$ ?at the parking lot under current conditions, determine the number of parking bays in the parking lot. Assume an efficiency factor of $0\mathrm{.}90.$

The owner of the parking lot is planning an expansion of the lot to provide adequate demand for the following $10$ ?years. If the owner has estimated that parking demand for all categories will increase by $5\%$ ?a year, determine the number of additional parking bays that will be required.

$5$