Question

If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the maximal area?

Answer 1

41 ft wide and 61.5 ft long

Explanation:

Let

Width = x ft

Length = y ft

Total fencing = 3 Width + 2 Lenght

So,

`3x+2y=246\\ \\2y=246-3x\\ \\y=123-1.5x`

Find the area:

`A(x)=x* y\\ \\=x(123-1.5x)\\ \\=123x-1.5x^2`

Find the derivative:

`A'(x)=123-2\cdot 1.5x=123-3x`

Equate it to 0:

`123-3x=0\\ \\3x=123\\ \\x=41\ ft\\ \\y=123-1.5\cdot 41=61.5\ ft`