A farmer must fence in a rectangular area for livestock. The total area needs to be 9000 square meters.

If fencing on the North and south sides of the pen costs 5$ per meter, and fences in the East and West sides will only cost 2$ per meter,

• Use calculus to determine the dimensions of the least expensive pen
• Find the cost of that pen.
• Show all of your work to justify your answer with calculus.