Chapter 4.7, Problem 31E

Supply from marginal supply. Stellar Lawn Care introduces a new kind of lawn seeder. It finds that its marginal supply for the seeder satisfies

$S^{\prime }\left(x\right)=\frac{100x}{{\left(20-x\right)}^2},0\le x\le 19$,

Where $S\left(x\right)$ is the quantity purchased when the price is x thousand dollars per seeder. Find $S\left(x\right)$, given that the company sells 2000 seeders when the price is 19 thousand dollars.

$S\left(x\right)=100\left[\frac{20}{20-x}+\text{In }\left(20-x\right)\right]$