Applied Optimization

Imagine you're tasked with constructing a rectangular pen for your cattle, and you have $496$ meters of fencing at your disposal. To economize on materials, you plan to utilize a steep cliff as one side of the pen, meaning you'll only need to fence in three sides. What's the maximum area you can enclose with the provided fencing? $($ could you explain every detail? Step by step$($i$.$e step $1..$ step $2..$ etc? $)$ im struggling here and would really appreciate the help to break this all down, i want to learn.. thank you$)$

$($a$)$ Draw a picture of the scenario. Make sure to define and label your variables.

$($b$)$ Write an equation that represents the area of the pen, and another equation that relates your two variables given the constraints of the problem.

$5pt.$

$($c$)$ Use your two equations from part $($b$)$ to write an equation for the area of the pen that involves only one variable.

$($d$)$ Use the equation from part $($c$)$ to solve for the maximum area.