# algebra

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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 -

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 -

3rd last line should say

= -2(x - 320)^2 + 204800

typo at the -2 in front, does not affect the answer.

• algebra -

dimensions: 320x640
max. area 204800

• algebra -

ergjoiso;gs;g

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