<PRE><B>Question 869920</B>
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

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