Question

{Will give medal} Quick question: How do I finish this problem?

A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $10 per foot and fencing for the other two sides costs $9 per foot. What is the maximum area that can be enclosed for $6000?

20L+18W=6000

18W = 6000 - 20L

W = 1000/3 - 10L/9

A = L*W

A = L (1000/3 - 10L/9)

A = 1000L/3 - 10L^2/9

Answer 1

Take the derivative of \(A\) with respect to \(L\):
\[\frac{dA}{dL}=\frac{1000}{3}-\frac{20L}{9}\]
and find the critical points (i.e. solve \(\dfrac{dA}{dL}=0\) for \(L\)).