Forming a pen: We want to form a rectangular pen of area 100 square feet. One side of the pen is to be formed by an existing building and the other three sides by a fence (see Figure 2.109). Let W be the length, in feet, of the sides of the rectangle perpendicular to the building, and let L be the length, in feet, of the other side.
a. Find a formula for the total amount of fence needed in terms of W and L.
b. Express, as an equation involving W and L, the requirement that the total area formed be 100 square feet.
c. Solve the equation you found in part b for L.
d. Use your answers to parts a and c to find a formula for F , the total amount, in feet, of fence needed, as a function of W alone.
e. Make a graph of F versus W.
f. Determine the dimensions of the rectangle that requires a minimum amount of fence.