# Thread: Applied Max/ Min Problems

1. ## Applied Max/ Min Problems

A rectangular garden laid out along a neighbour's lot contains 432 m^2. It is to be fenced on all sides. If the neighbour pays for half the shared fence, what should be the dimensions of the garden so that your cost is a minimum??

This is area = A'=0 is the derivative/
So A = l x w...........................so notes on the side is w x l = 432.

Where I am stuck is that do I take half of L and half of W for the equation??
So I use A = l/2 X w/2??

Answer is 18 x 24 m.
STUCK!!

2. total cost is based on the perimeter of the garden ...

$C_T = 2L + 2W$

let $L$ be the shared side ... neighbor's cost is $\dfrac{L}{2}$ . Your cost ...

$C = \dfrac{3L}{2} + 2W$

note that $W = \dfrac{432}{L}$ ...

$C = \dfrac{3L}{2} + \dfrac{864}{L}$

find $C'$ and determine the value of $L$ that minimizes $C$