Problem: The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed v. A certain ferry boat uses $196 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is $1323 per hour.
(a) Find the proportionality constant for the cost of the fuel per hour.
(b) Express the cost per mile in terms of v only.
(c) At what speed should the boat travel so as to minimize the cost per mile traveled?
I really don't know how to set up an equation for this, or how to find the proportionality constant. If somebody could explain to me how to interpret this problem, I think that's really all I'm missing here. I just need help getting an equation to differentiate, as well as help getting the proportionality constant.