Many real-life problems can be analyzed from a graphical, a numerical, and an analytical perspective. In this project, you will use all three strategies to determine the maximum size
of a rectangular plot that can be enclosed by a fixed amount of fencing. You have 200
meters of fencing material to enclose a rectangular plot. Your goal is to determine the
dimensions of the plot such that you enclose the maximum area possible.
a. (5 points) Express the area 4(x) of the rectangular plot as a function of the length x
of one side, as show in the figure below.
A(x)=x(100-x)
b
(3 points) Analyze the problem numerically by completing the table.
x
0
5
10
15
20
25
30
35
40
45
50
Please show your work as to how you got your values of A(x)
C. (2 Points) According to this table, what do you think the dimensions of the plot should
be to enclose the maximum area? Explain.
d. (2 points) Graph the area function from the values given in the table. Sketch the graph
below. Be sure to label your axes.