The question is as follows:

"A Farmer encloses three adjacent rectangular corrals with 1500 feet of fencing. Determine the length and width that will yield a maximum area."

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- Oct 9th 2013, 01:26 PMpromackHow do I begin to solve this problem?
The question is as follows:

"A Farmer encloses three adjacent rectangular corrals with 1500 feet of fencing. Determine the length and width that will yield a maximum area." - Oct 9th 2013, 01:48 PMtopsquarkRe: How do I begin to solve this problem?
The perimeter of the fence is a rectangle, of length x and width y, so we have 2x + 2y = 1500. The area is A = xy.

How can you put the area of the corral in terms of one variable? How do you go about finding a maximum area?

-Dan - Oct 9th 2013, 01:53 PMpromackRe: How do I begin to solve this problem?
it's 3 adjacent corrals though (imgur: the simple image sharer). Don't I have to somehow account for the fence that goes between the corrals?

- Oct 9th 2013, 02:01 PMHallsofIvyRe: How do I begin to solve this problem?
There are two long fences. Calling each length "x", their lengths total 2x. There are

**four**fences connecting them, two at the ends, two separating the three pens. If we call the length of each "y", their length total 4y. The total fencing is 2x+ 4y= 1500 feet and the area is xy square feet. You want to maximize xy subject to the constraint 2x+ 4y= 1500 feet.

One way to do that is to solve 2x+ 4y= 1500 for x= 750- 2y and write the area as $\displaystyle xy= (750- 2y)y= 1500y- 2y^2$. You can find the maximum by completing the square. - Oct 9th 2013, 02:05 PMSlipEternalRe: How do I begin to solve this problem?
How are the corrals set up?

Are they adjacent like this:

$\displaystyle \begin{tabular}{|c|c|c|}\hline & & \\ \hline\end{tabular}$

Or like this:

$\displaystyle \begin{tabular}{|c|c|}\hline & \\ \hline \multicolumn{2}{|c|}{ } \\ \hline \end{tabular}$

Should the corrals all be the same size?

Edit: I just saw the picture posted by the OP. I guess this post is moot. - Oct 9th 2013, 03:06 PMHallsofIvyRe: How do I begin to solve this problem?
- Oct 9th 2013, 04:33 PMpromackRe: How do I begin to solve this problem?
So I solved it and got the length as 375 feet and the width as 187.5 feet. Am I correct?

- Oct 9th 2013, 06:24 PMSlipEternalRe: How do I begin to solve this problem?