Chapter 3.2, Problem 96E

Advertising. A model for consumer’s response to advertising is given by

$N\left(a\right)=1000+200\ln a,a\ge 1,$ where $N\left(a\right)$

is the number of units sold and a is the amount spent on advertising, in thousands of dollars.

a. How many units were sold after spending $1000 on advertising?

b. Find $N\text{'}\left(a\right)$ and $N\text{'}\left(10\right)$

c. Find the maximum and minimum values on N, if they exist.

d. Find $N\text{'}\left(a\right)$. Discuss $\underset{a\to \infty }{\lim }N\text{'}\left(a\right)$. Does it make sense to spend more and more on advertising? Why or why not?