Suppose a farmer has 400 feet of fencing, and she wants to enclose a section of her ground that borders a river. The area enclosed will be a rectangle, but only three sides will be enclosed by the fence as the other side will be bounded by the river. This question will guide you through finding the maximum area the farmer can enclose.

a) Draw a picture of the situation on a piece of paper. Let $w$ and $l$ denote the width and length, respectively, of the enclosed rectangular field, with the width parallel to the river. What is the area of the enclosed region? (Enter your answer as a formula.)
$A =$

b) Assuming the farmer uses all 400 feet of available fencing, write an equation that gives the perimeter of the fence around the enclosed space. (Enter your answer as a formula.)
$400=$

c) Solve for $w$ in your equation in part (b).
$w =$

d) Plug your result from part (c) into your formula in part (a). You should now have a quadratic equation that uses only one variable. What is it?
$A(l)=$

e) Find the vertex of the parabola in part (d).
Vertex: $($ , $)$
Is this vertex a minimum or a maximum? ? Maximum Minimum

f) What is the maximum area that the farmer can enclose?
Maximum area: ? feet square feet
What values of $l$ and $w$ should he choose to attain this maximum?
$l =$
$w =$

Hint: