Posted by Anonymous on Tuesday, November 30, 2010 at 4:59pm.
a local grocery store has plans to construct a rectangular parking lot that is bordered on one side by a highway. there are 1280 feet of fencing avaliable to enclose the other three sides. find the dimensions that will maximize the area of the parking lot.

algebra  Reiny, Tuesday, November 30, 2010 at 5:50pm
Let the length be y ft and the width be x ft.
(I am looking at 2 widths and 1 length)
so y + 2x = 1280
y = 12802x
Area = xy
= x(12802x)
=  2x^2 + 1280x
complete the square ....
Area =  2(x^2  640x + 102400  102400)
=  (x  320)^2 + 204800
so x = 320 , then y = 1280640 = 640
the width is 320 ft, and the length is 640 ft

algebra  Reiny, Tuesday, November 30, 2010 at 5:51pm
3rd last line should say
= 2(x  320)^2 + 204800
typo at the 2 in front, does not affect the answer.

algebra  cait, Wednesday, December 12, 2012 at 4:35pm
dimensions: 320x640
max. area 204800

algebra  Anonymous, Saturday, November 8, 2014 at 12:09pm
ergjoiso;gs;g
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