$20-43$ Incentive Pay Formula Development A restaurant manager has the following goals: $(1)$ serve $300$ customers per day and $(2)$

achieve an average price per customer of $$6\mathrm{.}88.$ The restaurant is open $365$ days per year. The two goals are equally important.

The manager's salary is $$68,000.$ The manager's incentive pay $($i$.$e$.,$ bonus$)$ should be $$12,800$ if both goals are achieved.

Required

Assuming the compensation function is linear, determine the following amounts in the contract:

a$.$ The rate per customer served, rounded to four decimal points.

b$.$ The rate per penny of average price per customer, rounded to four decimal points.

Independent of your answer to requirement $1,$ assume that the rate is $$0\mathrm{.}0763$ per customer served and $$11\mathrm{.}4451$ per penny of average

price per customer. Calculate the manager's total compensation if the restaurant serves $280$ customers per day at an average price of

$$6\mathrm{.}75.$ Round your final answer to the nearest dollar.