Set Pens
What is the largest possible area of 5 pens with 600ft of fencing?
A rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. He has 600 feet of fencing available to complete the job. What is the largest possible total area of the five pens?
How do you set up a problem like this to find area?
consider the entire figure:
You have a rectangle with 4 lines going though the middle (to subdivide it into 5 pens). Let x be the side parallel to the middle fences, and let y be the other side. Note that, by the confines of the problem,
2y + 2x + 4x = 600, since you have 600 ft of fencing. This simplifies to:
2y + 6x = 600
y = 300 - 3x
This is useful because now you can write the total area of the rectangle as
A = xy = x(300 - 3x) = 300x - 3x^2
Now, finding the maximum is just a matter of differentiating and finding the critical points:
A' = 300 - 6x = 0
6x = 300
x = 50
Thus, your maximum area occurs when you choose a length x of 50. Your total area is:
A = x(300 - 3x) = 50(150) = 7500 square feet
Thank you for the correction Siress 
good luck ranching!
SAKURA-Pigma Micron Pens. 6-Set (1 each): Black 005.20mm; Black 01.25mm; Black 02.30mm; Black 03.35mm; Black 05.45mm; Black 08 .50mm. A fine point drawing and writing pen offering a waterproof quick drying pigment ink...
|
|
This set includes: 12 opaque gel pens 12 glitter pens 12 metallic pens and 12 mixables (which are two colors in one pen that mix when the ink is layed down). Acid free.
|
|
SHEAFFER-Classic Calligraphy Kit: 21pc. A party in a box for the dedicated Calligrapher of any level! Three pens each with a different nib grade and a generous assortment of ink colors allow for multiple colors on the same project without cleaning the pen...
|
|
The sado-booty ring-master, theromantic toe sniffler, the gangster of dsp is back again! That's right, hymen records and cock rock disco are proud to present the vinyl version of his new full length album: 'oozing bass spasms'...
|
|
When the book of hip-hop is written, the world famous Beatnuts will have the right to an entire chapter. To understand them is to understand hip-hop music in its rawest inception. No bling-bling, no trendy sounds of the moment and no less than a good time is what's come to be expected from these diversified beat-makers...
|
|
GertrudWinner of the Venice Film Festival, Dreyer's last film is said to be both a celebration of free will and the tragedy of a lifeOrdetAs one of Carl Dreyer's most celebrated forays into the sound film, this Golden Globe winner deals directly with the spiritual theme first put forth in The Passion of Joan of Arc: personalized faith versus organized religion...
|
|
Pratfall-prone Rob Petrie (Dick Van Dyke) and his plucky wife Laura (Mary Tyler Moore), along with wisecracking co-workers Sally (Rose Marie) and Buddy (Morey Amsterdam), captured America's hearts in this TV favorite that irresistibly combined wit and slapstick...
|
|
MMM17201OF Ideal for hanging pictures without nail holes, interlocking fastener adheres firmly to flat surface. Removes cleanly without surface damage. Global Product Type: Mounting Tape; Hanger/Hook Type: N/A; Holds: Up to 3 lbs...
|
|
US $36.85
![20 OFF] New Mini Pocket Pen Fish Fishing Rod Set Gift](http://thumbs.ebaystatic.com/pict/220664961000_0.jpg)
![Milk Me [Vinyl]](http://www.pushpinproductions.com/images/i/51lt7wQoz5L._SL160_.jpg)
![The Carl Dreyer Collection (Gertrud, Ordet, The Passion of Joan of Arc) [VHS]](http://www.pushpinproductions.com/images/i/214BF9MTJDL._SL160_.jpg)
![The Dick Van Dyke Show - Season Three Box Set [VHS]](http://www.pushpinproductions.com/images/i/51EFY73NCNL._SL160_.jpg)
![The Kevin Costner Collection (Tin Cup, The Bodyguard, Robin Hood: Prince of Thieves) [VHS]](http://www.pushpinproductions.com/images/i/21F6RD9SWVL._SL160_.jpg)
