Answer
The required cost of fencing along the three sides as a function of the lot’s length $x$ is $C=25x+\frac{600,000}{x}$.
Work Step by Step
The area of the rectangle is:
$\begin{align}
& A=xy \\
& 60000=xy
\end{align}$
Solve for $y$ ,
$y=\frac{60000}{x}$
An expensive fencing along the lot’s front length costs $\$25$ per foot. An inexpensive fencing along the two side widths costs only $\$5$ per foot.
The cost is:
$C=25x+5\left( 2y \right)$
Now, the cost $C$ of fencing along the three sides as a function of length $x$ is found as follows.
Substitute $y=\frac{60000}{x}$ ,
$\begin{align}
& C=25x+5\left( 2y \right) \\
& =25x+5\left( 2\left( \frac{60000}{x} \right) \right) \\
& =25x+10\left( \frac{60000}{x} \right) \\
& =25x+\frac{600,000}{x}
\end{align}$
Hence, the cost of fencing along the three sides as a function of the lot’s length $x$ is $C=25x+\frac{600,000}{x}$.
