Forming a pen: We want to form a free-standing rectangular pen. Let W be the width, in feet, and L the length, in feet. Let F be the total amount of fence needed. Assume the total area of the pen will...

Forming a pen: We want to form a free-standing rectangular pen. Let W be the width, in feet, and L the length, in feet. Let F be the total amount of fence needed. Assume the total area of the pen will be 144 square feet.

a. Write a formula for F in terms of W and L.

 b. Express, as an equation involving W and L, the requirement that the total area of the pen be 144 square feet.

c. Solve the equation you found in part b for W.

d. Use your answers to parts a and c to find a formula for F in terms of L alone.

e. Make a graph of F versus L for values of L up to 24 feet.

f. Determine the dimensions of the pen that require the minimum amount of fence. Explain how your graph from part e illustrates or confirms your answer.