Question

Suppose a farmer has 2400 feet of fence and wishes to create two rectangular pens of the same dimensions with the two pens sharing one side (i.e. since the pens share one side, there is a total of 7 sides of fence). What is the maximum area of each of the pens?

Answer 1

The maximum area for each pen is 360,000 square feet.

Step-by-step explanation:

To find the maximum area of each rectangular pen, we need to find the dimensions that will give us the largest area.

1. Let's assume the width of each pen is x feet.
2. Since the two pens share one side, the length of each pen will be (2400 - 3x) / 2 feet.
3. The area of each pen is the width multiplied by the length, so we have: Area = x * (2400 - 3x) / 2.
4. To find the maximum area, we need to find the value of x that maximizes the function. We can do this by taking the derivative of the function with respect to x, setting it equal to zero, and solving for x.
5. After finding the critical points, we can evaluate the function at those points to determine the maximum area.

The maximum area for each pen is 360,000 square feet.