Then, we have
S(x) =
2
5
5
100
100
x
x
x
x


−
=
−




and
C(x) =
500
5
x +
Thus, the profit function P(x) is given by
P(x) =
2
S( )
C( )
5
500
100
5
x
x
x
x
x
−
=
−
−
−
i e P(x) =
2
24
500
5
100
x −x
−
or
P′(x) = 24
5
x50
−
Now P′(x) = 0 gives x = 240 Also 
1
P ( )
50
x
−
′′
=