1. ## Extreme Value Problems

A farmer wants to fence an area of $600m^2$ in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can this be done to minimize the cost of this fence?

$A = L \times w$

$600 = L \times w$

$\frac {600}{L} = w$

$P = 2L + w$

$P = 2L + \frac {600}{L}$

$P' = 2L - \frac {600}{L^2}$

$\frac {600}{L^2} = 2$

+/- $\sqrt{300} = L$

I stopped here because the answers in the textbook for length (which is 30m) is different and I don't know where I went wrong. Please help me?

2. Always draw a diagram...

There perimeter should be

$P=2w+3l$

Good luck.