Problem:The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speedv. 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 ofvonly.

(c) At what speed should the boat travel so as to minimize the costper miletraveled?

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 tointerpretthis 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.

Thank you!