I got half of this problem wrong and I DO NOT know where and how to fix. I cannot use my calculator and have to show my work.
Question: You have a 500 metre roll of fencing and a large field. You want to construct a rectangular playground area.
a.) using optimization techniques, find the dimensions of the largest such yard.
b.) calculate the largest area of the fenced play ground available.
Please help and show work, so I can see where I went wrong.
pick any sides x and y.
You will see that the largest area for a given perimeter is always a square.
In this case,
y = 250-x
a = xy = x(250-x) = 250x - x^2
da/dx = 250-2x
da/dx=0 when x=125
So, the rectangle is 125x125, a square
A good check on all these fencing problems, even those with multiple interior fences, is to note that the fencing is divided up evenly among the langths and widths.