Answer
(a.) The profit function is $ P(x)=20x-10,000 $
(b.) Profit $ =\$ 190,000 $.
Work Step by Step
Cost function $ C(x)=10,000+30x $
and Revenue function $ R(x)=50x $
(a.)
Profit function $=$ Revenue function $- $ cost function.
$ P(x) = R(x)-C(x)$
Substitute values.
$ P(x)=50x-(10,000+30x) $
$ P(x)=50x-10,000-30x $
$ P(x)=20x-10,000 $
(b.) Substitute $ x=10,000 $ into profit funciton.
$ P(10,000)=20(10,000)-10,000 $
$ P(10,000)=200,000-10,000 $
$ P(10,000)=190,000 $.
