A farmer wishes to put a fence around a rectangular field and then divide the field into four rectangular plots by placing three fences parallel to one of the sides. If the farmer can afford only 2500 yards of fencing, what dimensions will give the maximum rectangular area?
2007-10-12 15:41:34 · 3 answers · asked by Anonymous in Education & Reference ➔ Homework Help
ask it in the math section
but you have 4(2a+b)+b=2500 from where you can factor out a or b to substitute in 4a*b=A then take the derivative of A, set that equal to 0 and you'll get a value for a or b, depending on how you made your substitution
use that value in the A formula and you'll get the maximum area for the big rectangle
2007-10-12 15:47:59 · answer #1 · answered by Anonymous · 1⤊ 0⤋
look at the total
he has 2500 yds to be the most he can use
the amount will be 2lenghths + 2widths + 3lengths
so 5 lengths and 2 widths = 2500 (or less)
We also want length x width to be the biggest
A square will use the least perimeter to create the most area (a circle is even better, but not a choice)
So now we have length = width
so 7 lengths = 2500
one is 2500/7
so the area will be 2500/7 x 2500/7 square yards
or, 127,551.02 yards ^2
each side is 357.14 yards
2007-10-12 22:45:19 · answer #2 · answered by ignoramus 7 · 0⤊ 0⤋
3x7 ;)
2007-10-12 22:46:03 · answer #3 · answered by ihavebling14 1 · 0⤊ 0⤋