Construction. A construction company has 840 feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical rectangular storage areas sharing a common fence (see the figure).
Assuming that all fencing is used,
(A) Express the total area A(x) enclosed by both pens as a function of x.
(B) From physical considerations, what is the domain of the function A?
(C) Graph function A in a rectangular coordinate system.
(D) Use the graph to discuss the number and approximate locations of values of x that would produce storage areas with a combined area of 25,000 square feet.
(E) Approximate graphically (to the nearest foot) the values of x that would produce storage areas with a combined area of 25,000 square feet.
(F) Determine algebraically the dimensions of the storage areas that have the maximum total combined area. What is the maximum area?