3. A farmer has a 150 feet of fencing and wants to construct 3 pig pens by first building a fence around a rectangular region, then subdividing the region into 3 smaller rectangles by placing 2 fences parallel to one side of the rectangle. What dimensions of the region maximizes the total area?

and

Step-by-step explanation:

The total perimeter and area of the pig pens are, respectively:

In order to know the maximum area, the second function shall be simplified, derived and equalized to zero. The solution leads to a critical point, whose characteristics can be deduced by using the second derivative of the area:

(absolute maximum)

The dimensions of the region that maximizes the total area are:

and

answer: do we write it

step-by-step explanation:

c. 1,233 miles