Acme Parking Garage charges cars a flat fee of $10 for parking any duration, in addition to a variable prorated rate of $5 per hour (as an example, a car staying 1.5 hours would be charged $17.50). Suppose the total throughput is measured in units of cars per hour, and INV is the average number of cars in the garage.

a. Express the average hourly revenue as a function of and/or INV. Acme decides to start a valet service. They will charge a flat fee of $40 for valet parking (that is, they are not charged an hourly rate) and pay valet staff $5 per car they park. Suppose the total customer base remains the same as before (i.e., is still the total throughput) but now 30% of all customers opt for the valet service.

b. Write the average hourly profit function (which excludes fixed costs, such as over- head and rent) as a function of and/or INVhourly and/or INVvalet (where INVhourly and INVvalet are the average number of hourly and valet cars parked in the garage, respectively.)