(1 pt) The owner of a garden supply store wants to construct a fence to enclose

Question

(1 pt) The owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 270 feet long, as one of the sides of the enclosed area. There are 450 feet of fencing available for the other three sides of the enclosure. Find the dimensions of the outdoor enclosure with the most area. Note: The answer to this problem requires that you enter the correct units storage area garden supply store Length of side parallel to store wall Length of a side perpendicular to store wall

Explanation / Answer

Since one side is the wall, we let x be perpendicular and y be parallel:
2x+y = 480

y=480-2x

Area is the the product of the two sides, thus.
xy=480x - 2x^2

for maximum, d(xy)/dx must be 0. thus,

480-4x=0

x= 120. thus, y = 240.

Since 240<280, the side of the store is not a constraint.

thus, the perpendicular sides are 120 feet long and the parallel side is 240 feet long.

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