(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

profit = revenue minus cost

3. The attempt at a solution

i know that --> P(x) = R(x) - C(x) and R(x) = xp(x)

i hate optimization and i really suck at it. i don't know how to get the equations if i get the equations then i know how to solve it. please help and thanks in advance.

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# Help with really hard optimization problem

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