posted by Anonymous .
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 = 1280-2x
Area = xy
= - 2x^2 + 1280x
complete the square ....
Area = - 2(x^2 - 640x + 102400 - 102400)
= - (x - 320)^2 + 204800
so x = 320 , then y = 1280-640 = 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.
max. area 204800