Data collected at a parking lot indicate that a total of $300$ cars park between $8$ a$.$m$.$ and$5$ p$.$m$.5\%$ of these cars are parked for an average of $2$ hr$,20\%$ for an average of $3$ hi$,10\%$ for an average of $4$ hr$,$ and the remaining cars are parked for an average of $9$ hr$.$a$.$ Determine the space$-$hours of demand at the lot.b$.$ If $10\%$ of the parking bays are vacant on average $($between $8$ 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 $0\mathrm{.}90.$c$.$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 $3\%$ a year, determine the number of additional parking bays that will be required.