Problema Solution
A rectangular enclosure is to be built using 1050 feet of fencing. The enclosure will also be divided into 5 sections, each the same size. What is the maximum possible area of this enclosure? And what are the dimensions of the enclosure?
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To solve this question, we will assume that the 5 sections have all of their lengths (6) parallel to each other such that some of the sections are sharing w as a boundary. Thus, the total fencing can be written as:
1050=6l+10w
or
l=(1050-10w)/6
Likewise, the area can be written as:
area=l(5w)
or
area=(1050-10w)(5w)/6
or
area=875w-(50/6)w^2
The derivative is:
area'=875-(100/6)w
We will set this equal to 0 to find the max.
0=875-(100/6)w
w=52.5
therefore
l=87.5