1. ## max min problem

rectangular plot of farm land will be bounded on one side by a river and the other 3 sides by a single strand of electric wire. With 800 metres of wire at your disposal what is the largest area you can enclose and what are its dimensions.

1st I let the perimeter = 800
2y+x= 800

then i subbed into the equation for the area A=xy and let it equal to zero.
but i got to differentiate is this wrong?
could someone verify my anwer?

2. ## Re: max min problem

Originally Posted by raoulduke1
rectangular plot of farm land will be bounded on one side by a river and the other 3 sides by a single strand of electric wire. With 800 metres of wire at your disposal what is the largest area you can enclose and what are its dimensions.

1st I let the perimeter = 800
2y+x= 800

then i subbed into the equation for the area A=xy and let it equal to zero.
but i got to differentiate is this wrong?
could someone verify my anwer?
You need the area to only be a function of one variable.

From the first equation, you have $\displaystyle 2y+x = 800 \implies y = 400 - \frac{1}{2}x$, so substituting into the second gives

\displaystyle \begin{align*} A &= xy \\ A &= x\left(400 - \frac{1}{2}x\right) \\ A &= 400x - \frac{1}{2}x^2 \\ \frac{dA}{dx} &= 400 - x \end{align*}

Now set the derivative equal to $\displaystyle 0$, solve, back-substitute, solve for $\displaystyle y$.