Question 62037: You are visiting your grandparents on their farm. They have asked you to design a small, rectangular-shaped vegetable garden along an existing wall in their backyard. they wish to surround the garden with a small fence to protect their plants from animals.
To enclose the garden, you have 15 yards of fencing. The fencing is sold in .6 yard panels. In order to grow as many vegetables as possible, your task is to design the fence to enclose the maximum possible area. Partial panels of fencing may not be used.
How many panels of fencing should you use along the width of the garden?
How many panels would you use along the length of the garden?
Justify your solution in complete sentences.
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I know that the length is 27 feet (15 panels) and the width is 9 feet (5 panels) each. Panels are 1.8 feet each. The wall is the 2nd length.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! To enclose the garden, you have 15 yards of fencing. The fencing is sold in .6 yard panels. In order to grow as many vegetables as possible, your task is to design the fence to enclose the maximum possible area. Partial panels of fencing may not be used.
How many panels of fencing should you use along the width of the garden?
How many panels would you use along the length of the garden?
Justify your solution in complete sentences.
:
The max area from 15 yds of fence without the panel restraint:
L + 2W = 15
L = (15-2W)
:
Area = (15-2W)*W
Area =-2W^2 + 15W
:
Find the axis of symmetry of this quadratic equation: x = -b/(2a)
W = -15/(2*-2)
W = -15/-4
W = +3.75 yds is the width for max area
:
L = 15-2(3.75)
L = 15 - 7.5
L = 7.5
:
Max area = 7.5* 3.75 = 28.125
:
15/.6 = 25 panels
3.75/.6 = 6.25 panels
:
How about 6 by 13 by 6 panels: Find the area, 6 by 13 panels:
.6(6) * .6(13) = 28.08 sq yds pretty close to max
However,
How about 7 by 11 by 7 panels.
.6(7) * .6(11) = 27.72 sq yds not quite as good
:
Go with 6 by 13 by 6 panels as the best way to go
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