Maximizing Profits: A construction company has been offered a contract for $7.8 million to construct and operate a trucking route for five years to transport ore from a mine site to a smelter. The smelter is located on a major highway and mine is 3 km into a heavily forested area off the road.
Construction (capital) costs are estimated as follows:
-Repaving the highway will cost $200000/km
-A new gravel road from the mine to the highway will cost $500000/km
Operating Conditions are as follows:
-There will be 100 round trips each day, for 300 days a year, for each of the five years the mine will be open.
-Operating costs on the gravel road will be $65/h, and the speed limit will be 40 km/h.
-Operating costs on the highway will be $50/h, and the speed limit will be 70 km/h.
Use calculus to determine if the company should accept the contract. Determine the average speeds of the trucks along the paved and gravel roads that produce optimum conditions (Maximum profit). What is the maximum profit?

Please Help me solve this Question and please explain the process and what you're doing. Please and Thank you!
There's also a picture with this question which you can find on:
http://www.flickr.com/photos/serahafreen/5548307797/
http://www.flickr.com/photos/serahafreen/5548307797/

Read this first: Expectations for the Homework Help board

--------------------------------------------------------------------------------

Do not simply retype or paste a question from your book or study material

We won't do your homework questions for you.
You were given the assignment for you to learn.

If you come up with your own answer and post it for us to critique that is within reason.

If you have some SPECIFIC questions that you couldn't find or didn't understand, we may help with that.
But this is your assignment, so show us you have at least attempted to complete it on your own.

Thank you.