Asked by Eva
A farmer has 1000 feet of fencing materials available to fence a rectangular pasture next to a river. If the side along the river does not need to be fenced, what dimensions maximize the enclosed area? What is the maximum enclosed area?
Answers
Answered by
Reiny
let side parallel to river be y
let the other two sides be x each
2x + y = 1000 , ----> y = 1000-2x
area = xy = x(1000-2x) = 1000x - 2x^2
if you know Calculus.....
d(area)/dx = 1000 - 4x
= 0 for a max of area
4x =1000
x = 250
y = 1000-2(250) = 500
so max area = xy = 250(500) = 125000 ft^2
let the other two sides be x each
2x + y = 1000 , ----> y = 1000-2x
area = xy = x(1000-2x) = 1000x - 2x^2
if you know Calculus.....
d(area)/dx = 1000 - 4x
= 0 for a max of area
4x =1000
x = 250
y = 1000-2(250) = 500
so max area = xy = 250(500) = 125000 ft^2