Answer
The consumer surplus is $407.25.
Work Step by Step
We can find the number of units $X$:
$p(x) = \frac{450}{x+8}$
$\frac{450}{X+8} = 10$
$450 = 10X+80$
$X = 37$
We can find the consumer surplus:
$\int_{0}^{X}[p(x)- P]~dx$
$=\int_{0}^{37}[ \frac{450}{x+8}- 10]~dx$
$=450~ln(x+8)- 10x~\vert_{0}^{37}$
$=450~ln(37+8)- 10(37)~- 450~ln(0+8)- 10(0)$
$=1713- 370- 935.75-0$
$= \$407.25$
The consumer surplus is $407.25
