• Apr 25th 2010, 08:13 PM
dorkymichelle
7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

$\displaystyle Y=\frac{kN}{1+N^2}$

where K is a positive constant. What nitrogen level gives the best yield?

I thought all optimization problems follow a basic, constraint and then a formula form.
I'm terrible at word problems, so I don't see where there is a constraint in this one?
• Apr 25th 2010, 08:20 PM
mr fantastic
Quote:

Originally Posted by dorkymichelle
7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

$\displaystyle Y=\frac{kN}{1+N^2}$

where K is a positive constant. What nitrogen level gives the best yield?

I thought all optimization problems follow a basic, constraint and then a formula form.
I'm terrible at word problems, so I don't see where there is a constraint in this one?

You're expected to realise that you start by solving dY/dN = 0.
• Apr 25th 2010, 08:22 PM
Prove It
Quote:

Originally Posted by dorkymichelle
7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

$\displaystyle Y=\frac{kN}{1+N^2}$

where K is a positive constant. What nitrogen level gives the best yield?

I thought all optimization problems follow a basic, constraint and then a formula form.
I'm terrible at word problems, so I don't see where there is a constraint in this one?
$\displaystyle Y = \frac{kN}{1 + N^2}$
$\displaystyle \frac{dY}{dN} = \frac{(1 + N^2)\frac{d}{dN}(kN) - kN\,\frac{d}{dN}(1 + N^2)}{(1 + N^2)^2}$