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

I have been stuck working on this problem for the past little while and can't seem to figure it out.

A construction company needs to create a trucking route for five years to transport ore from a mine site to a smelter. The smelter is located on a major highway 10km from where the mine is 3km off the road.

Construction Costs:

- Upgrade highway costs $200 000/km
- Build new gravel road from mine to highway is $500 000/km

Operating conditions:

- There will be 100 return trips each day for 300 days in a year for 5 years
- Operating costs on the gravel road will be $65/h and average speed of 40km/h
- Operating costs on the highway will be $50/h and a average speed of 70km/h

Edit: Forgot to mention the book says not to consider the time value of money in your calculations.

2. Relevant equations

Pythagorean Theorem: c^2=a^2+b^2

3. The attempt at a solution

I figured first I need to figure how to construct the route from the mine on the gravel road and highway. Using a Pythagorean I came up with this equation for the cost to build the road: C(x)=500 000[tex]\sqrt{x^2+3^2}[/tex]+200 000(10-x). Now I'm not sure if I should include operation into the above equation or just make a separate equation all together. I tried to make one big equation into the formula, but I found it confusing and wasn't sure what equation represented. Any help is appreciated.

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# Optimization Problem

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