Final answer:
To find the dimensions that maximize the area of Kojo's plan, set up an equation based on the given information and solve for the relationship between length and width. Then, express the area in terms of a single variable and use calculus to find the maximum area.
Step-by-step explanation:
To find the dimensions that maximize the area of Kojo's plan, we can use the given information that 500 units of fencing are available to make 4 rectangle pens of identical shape.
Let's assume the length of each pen is L and the width is W.
The perimeter of each pen is given by the formula 2L + 2W. Since there are 4 pens, the total fencing used would be 4 times the perimeter, which is 4(2L + 2W).
Since we know that the total available fencing is 500 units, we can set up the equation 4(2L + 2W) = 500 and solve for L in terms of W or vice versa.
Once we have the relationship between L and W, we can express the area of each pen as A = L * W. Then, using the relationship between L and W, we can express A in terms of a single variable and use calculus to find the maximum area.