SOLUTION: A farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the entire area and then subdivide it by running a perpendicular fence across the middle. Find the

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Question 869920: A farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the entire area and then subdivide it by running a perpendicular fence across the middle. Find the dimensions of the field that would enclose the maximum area. What is the maximum area?
Can you please help me out? Thank you so much in advance:)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer has 3000 feet of wire to enclose a rectangular field. He plans to fence the entire area and then subdivide it by running a perpendicular fence across the middle. Find the dimensions of the field that would enclose the maximum area. What is the maximum area?
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let x=length of rectangular field
let y=width of rectangular field
amount of wire required=2*length+2*width+fence across middle=2x+2y+y=2x+3y=3000
3y=3000-2x
y=-(2/3)x+1000
Area=x*y=-(2/3)x^2+1000x
complete the square:
Area=-(2/3)(x^2-1500x+(750^2))+375000
Area=-(2/3)(x-750)^2+375000
This is an equation of a parabola that opens downward with vertex at (750, 375000)
x=750
y=-(2/3)x+1000=-500+1000=500
..
Overall dimensions of the field: 750 ft by 500 ft
maximum area=375,000 sq ft