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Related Rates Problem

Your company is going to ship old calculus textbooks to be pulped and recycled. You hire a driver at a flat rate of 3 per gallon for fuel. Your truck gets 600/x miles per gallon when driven at a constant speed of x miles per hour (between 50 and 70 mph). What speed should you ask your driver to maintain (between 50 and 70 mph) to minimize your costs per mile driven?

We've been asked to minimize the "cost per mile driven". That means we need to turn our word equations into proper equations and get them in terms of "cost per mile driven". We can write "cost per mile" driven as just where is cost and is distance. So the first bit for the drivers pay is where is cost for the drivers pay and is time in hours. We also know that distance is speed times time. So we have or . We can combine these to get . Rearranging to get in terms of leads us to . What do you think the next stage is?
31 October 2011
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