Chapter 3, Problem 41RE

To determine

Largest area that can be enclosed.

Answer to Problem 41RE

Largest area is $4167500m^2$ .

Explanation of Solution

Given information:

fencing $=10000m$

Calculation:

  $\begin{array}{l}10000=3x+2y\\ y=5000-\frac{3x}{2}\\ A=xy=x\left(5000-\frac{3x}{2}\right)\\ A=\frac{3x^2}{2}+5000x\end{array}$

For max:

  $\begin{array}{l}A:x=\frac{-b}{2a}=\frac{-5000}{-3}=1667\\ y=2500\\ A=xy\\ =1667\times 2500\\ A=4167500m^2\end{array}$

Thus, $x=1667$ and $y=2500$ . And largest area is $4167500m^2$ .