Final answer:
To maximize the area of Kojo's plan, the dimensions should be a length of 0 units and a width of 166.67 units. To maximize the area of Ama's plan, the dimensions should be a length of 0 units and a width of 83.33 units. The best plan that maximizes the area is Ama's plan with dimensions of 0 units by 83.33 units.
Step-by-step explanation:
To maximize the area, we need to find the dimensions of the rectangles that use up all the available fencing. Let L be the length of each rectangle and W be the width. Since we have four rectangles, the total fencing used is 2L + 6W = 500. From this equation, we can express L in terms of W as L = 250 - 3W/2.
To maximize the area, we need to find the dimensions that result in the largest possible value for LW. We can do this by finding the critical points of the function LW.
Taking the derivative of LW with respect to W and setting it equal to zero to find the critical points, we get d(LW)/dW = 250 - 3W/2 = 0. Solving this equation, we find W = 166.67.
Substituting this value of W into the equation for L, we get L = 250 - 3(166.67)/2 = 250 - 250 = 0.
Therefore, to maximize the area of Kojo's plan, the dimensions should be a length of 0 units and a width of 166.67 units.
To find the dimensions that maximize the area of Ama's plan, we can use a similar approach. Let L' be the length of each rectangle and W' be the width. The total fencing used is 2L' + 6W' = 500. From this equation, we can express L' in terms of W' as L' = 250 - 3W'.
Taking the derivative of L'W' with respect to W' and setting it equal to zero to find the critical points, we get d(L'W')/dW' = 250 - 3W' = 0. Solving this equation, we find W' = 83.33.
Substituting this value of W' into the equation for L', we get L' = 250 - 3(83.33) = 250 - 250 = 0.
Therefore, to maximize the area of Ama's plan, the dimensions should be a length of 0 units and a width of 83.33 units.
The best plan that maximizes the area is Ama's plan with dimensions of 0 units by 83.33 units. This is because a width of 83.33 units allows for a longer length and therefore a larger area, compared to the width of 166.67 units in Kojo's plan which results in a length of 0 units and zero area.