Stop$-$n$-$Shop operates a downtown parking lot containing $800$ parking spaces. The lot is open $2,500$ hours per year. The parking charge per car is $50$ cents per hour; the average customer parks two hours. Stop$-$n$-$Shop rents the lot from a development company for $$7,250$ per month. The lot supervisor is paid $$24,000$ per year. Five employees who handle the parking of cars are each paid $$300$ per week for $50$ weeks, plus $$600$ each for the two$-$week vacation period. Employees rotate vacations during the slow months when four employees can handle the reduced load of traffic. Lot maintenance, payroll taxes, and other costs of operating the parking lot include fixed costs of $$3,000$ per month and variable costs of $5$ cents per parking$-$space hour.

Required:

b$.$ What is the contribution margin ratio? What is the annual break$-$even point in dollars of parking revenue?

c$.$ Suppose that the five employees were taken off the hourly wage basis and paid $30$ cents per car parked, with the same vacation pay as before. $(1)$ How would this change the contribution margin ratio and total fixed costs? $($Hint: The variable costs per parking$-$space hour will now include $15$ cents, or one$-$half of the $30$ cents paid to employees per car parked, because the average customer parks for two hours.$)(2)$ What annual revenue would be necessary to produce operating income of $$300,000$ under these circumstances?