SOLUTION: A farmer wants to create four rectangular corral's to separate his livestock. He has 750m of fencing to create the corrals as seen below. If the rancher wants the total area to be
Question 1137646: A farmer wants to create four rectangular corral's to separate his livestock. He has 750m of fencing to create the corrals as seen below. If the rancher wants the total area to be a maximum, what dimensions should be used to make the corral's? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A farmer wants to create four rectangular corral's to separate his livestock.
He has 750m of fencing to create the corrals as seen below.
If the rancher wants the total area to be a maximum, what dimensions should be used to make the corral's?
:
let L = the overall length of the corral
let w = the width of which there will be 5, in order to have 4 corrals
:
L + 5w = 750
arranged for substitution
L = -5w + 750
Area
A = L*w
replace L with (-5w+750)
A = (-5w+750)*w
A = -5w^2 + 750w, a quadratic equation where, a=-5,b=750
Max area occurs on the axis of symmetry, find that w = -b/(2a)
w =
w = +75 meters is the width for max area
then
L = -5(75) = 750
L = -375 + 750
L = 375 meters is the length
