Optimal fencing
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For each of the following methods of fencing,
find the maximum possible area for a fixed length
of fence.
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For each method of fencing, show that
a relevant correspondence rule can be constructed as a
product of linear functions.
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Which of the proposed methods would you
choose to obtain the maximum fenced area for a fixed length
of fence?
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You have 40 meters of fence. Determine the
maximum area that can be fenced in the
shape of a half circle adjoined to a rectangle (see figure):
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a.
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You have 40 meters of fence. Determine the
maximum area that can be fenced in the
shape of two half circles adjoined to a rectangle (see figure):
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You have 40 meters of fence. Determine the
maximum area that can be fenced in the
shape of an equilateral triangle adjoined to a rectangle (see figure):
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You have 40 meters of fence. Determine the
maximum area that can be fenced in the
shape of two equilateral triangles adjoined to a rectangle (see figure):
| d. |
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