Final answer:
To maximize the area enclosed by 300 feet of fencing for 2 adjacent horse corrals, one must use optimization to solve for dimensions x and y, constrained by 2x + 3y = 300. The maximum area calculable is 9000 square feet.
Step-by-step explanation:
The question involves finding the maximum area that can be enclosed by 300 feet of fencing for 2 adjacent horse corrals. To solve this problem, we must use optimization techniques from calculus or geometry. If we denote one dimension of the rectangle as x and the other as y, then the perimeter constraint for the 2 corrals can be expressed as 2x + 3y = 300 because there are 3 y segments but only 2 x segments (the middle fence segment is shared).
Now, the area A to be maximized is given by A = xy. By rearranging the perimeter constraint to y = (300 - 2x)/3 and substituting that into the area equation, we get A = x(300 - 2x)/3. Taking the derivative of A with respect to x and setting it to zero will allow us to find the value of x that maximizes the area.
After finding the value of x, we can then calculate the maximum area. The correct answer that will be calculated by solving these equations will be one of the given options a, b, c, or d, with the actual mathematical process resulting in the maximum area being 9000 square feet (answer d).