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 = 1280-2x

Area = xy

= x(1280-2x)

= - 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

- 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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