# calculus

this is a optimization problem
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 the mine is 3 km into a heavily forested area off the road.
Construction (capital) costs are estimated as follows:
•Repaving the highway will cost \$200 000km.
•A new gravel road from the mine to the highway will cost \$500 000km.
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 \$65h, and the speed limit will be
40 kmh.
•Operating costs on the highway will be \$50h, and the speed limit will be
70 kmh.
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?

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