Question

A rectangular plot of ground is to be enclosed by a fence and then divided down the middle by another fence. If the fence down the middle costs $3 per running foot and the other fence costs $4 per running foot, then find the largest possible area with $880.00 worth of fence:

Answer 1

The following solution is from Mathematica's Constrained Optimization feature. 9680/3 is the maximum area.
\[\text{Maximize}[\{x y,10 x+6 y=880,x>0,y>0\},\{x,y\}] \]\[\left\{\frac{9680}{3},\left\{x\to 44,y\to \frac{220}{3}\right\}\right\} \]