A farmer wants to fence a rectangular area as inexpensively as possible. Assume that fencing materials cost $1 per foot.
a) Suppose that $40 is available for the project. How much area can be enclosed?
b) Suppose that 100 square feet must be enclosed. What is the least possible cost?
c) Discuss the relation between the two parts above. Did the two approaches give the same result?
Area and cost are optimized by applying derivatives. The solution is detailed and well presented.