Question

Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing.

If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.

Answer 1

80000 ft^2 or about two acres

Explanation:

p + 2 q = 800 so p = 800 - 2 q

A = p q = (800 - 2q)q

A = -2 q^2 + 800 q

Find the vertex of this parabola by completing the square

dA/dq = 0 at max = -4 q + 800

or

q = 200

then

p = 800 - 400 = 400

so

A = 80,000 ft^2

Sorry if this is confusing if you have questions, reply to this!