algebra
posted by Anonymous on .
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.

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 
3rd last line should say
= 2(x  320)^2 + 204800
typo at the 2 in front, does not affect the answer. 
dimensions: 320x640
max. area 204800 
ergjoiso;gs;g