document.write( "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? \r
\n" ); document.write( "\n" ); document.write( "Can you please help me out? Thank you so much in advance:) \n" ); document.write( "
Algebra.Com's Answer #524574 by lwsshak3(11628)\"\" \"About 
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?
\n" ); document.write( "***
\n" ); document.write( "let x=length of rectangular field
\n" ); document.write( "let y=width of rectangular field
\n" ); document.write( "amount of wire required=2*length+2*width+fence across middle=2x+2y+y=2x+3y=3000
\n" ); document.write( "3y=3000-2x
\n" ); document.write( "y=-(2/3)x+1000
\n" ); document.write( "Area=x*y=-(2/3)x^2+1000x
\n" ); document.write( "complete the square:
\n" ); document.write( "Area=-(2/3)(x^2-1500x+(750^2))+375000
\n" ); document.write( "Area=-(2/3)(x-750)^2+375000
\n" ); document.write( "This is an equation of a parabola that opens downward with vertex at (750, 375000)
\n" ); document.write( "x=750
\n" ); document.write( "y=-(2/3)x+1000=-500+1000=500
\n" ); document.write( "..
\n" ); document.write( "Overall dimensions of the field: 750 ft by 500 ft
\n" ); document.write( "maximum area=375,000 sq ft\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );