Given model, find units sold, N' and N'', and min/max

[manuel1]

A model for advertising response is given by

N(a) = 3000 + 500 ln a, a ≥ 1

where N(a)= the number of units sold and a= the amount spent on advertising, in thousands of dollars.

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

b. Find N'(a) and N''(10)

c. Find the minimum and maximum number of units sold (if they exist), and the amount of advertising dollars that produces the minimum and maximum (if they exists)


Please help

 

[tkhunny]

That's the fifth problem in five minutes with no work shown. I'm beginning to become suspicious about the name changing every other post.

What's it going to be, manuel1? Show your work and prove me wrong or allow me to go with my assumptions?

 

[ladyazpy]

here is my work

a. N(1)= 3000+500 ln1=3000
3000 units

b. N(a)= 500 (1/a) = 500/a

N(10)= 500 (1/10) = 500/10 or 50

c. No critical points
N(1) = 3000

N(∞)= lim as a goes to ∞ =(3000 + 500 ln a

Minimum value is 3000 when a = 1

 

[stapel]

Subject line: here is my work

How could this be "your" work, when somebody else posted the question...? :shock:

Thank you!

Eliz.