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Profit Functions: Carwash

SATMAT-XK1KDV

A carwash finds that it loses customers as it increases the price for washing a car. In particular, the function $ c(p)=-4p+100 $ models the number of customers $ c $ who come in each day as a function of the price, $ p $, for washing a car.

If the carwash has a flat daily operating expense of ${\$500}$, which function models the carwash's daily profit, $ D $, as a function of $ p $?

A

$ D(p)=-4p-400 $

B

$ D(p)={ -4p }^{ 2 }+100p-500 $

C

$ D(p)={ -4p }^{ 2 }+100p $

D

$ D(p)={ -4p }^{ 2 }-500 $