I'm working my way through Thompson's Calculus Made Easy, and I'm stuck on a problem in Chapter 11:

Suppose it to be known that consumption of coal by a certain steamer may be represented by the formula

y=0.3 + 0.001v^3

where y is the number of tons of coal burned per hour and v is the speed expressed in nautical miles per hour. The cost of wages, interest on capital, and depreciation of that **** are together equal per hour to the cost of one ton of coal. What speed will make the total cost of a voyage of 1,000 nautical miles a minimum? And if coal costs ten dollars per ton, what will that minimum cost of the voyage amount to?

OK, so I realize that we have to express the first

equation in terms of cost (C). If the added expense of wages, interest, etc. per hour are equal to one ton of coal burned per hour, then I think that the cost would equal 2y or:

C=0.6 + 0.002v^3

Is this correct? And what should my next step be? In view of the 1,000 mile trip, should I change v^3 to (m/h)^3 and plug that in? I'm not sure how to proceed.

Thanks!

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