Chapter 2, Problem 90RE

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 $A\left(x\right)$ 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?