Build a rectangular pen with three parallel partitions (meaning 4 total sections) using 500 feet of fencing. What dimensions will maximize the total area of the pen?
1 Answer
The dimensions that will maximize the area the total area of the pen will be
Total area with these dimensions:
Explanation:
Step 1: Set up a picture/diagram to help answer the question and write out the needed equations.
Diagram:
The total length will be
Needed Equations:
Perimeter of this diagram
Total Area
Step 2: Solve for
Step 3: Substitute the equation for
Step 4: Find the derivative of the equation for area.
Step 5: Use the derivative equation in order to find the critical point(s) that maximize the area.
Critical points are when
Since
Step 6: Find the height (
The dimensions that will maximize the area the total area of the pen will be
Step 7: Find the total area of the pen.