Question

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 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 $700 per hour. At what speed should it travel so as to minimize the cost per mile traveled?

(Hint: What is the relationship between cost per mile, cost per hour, and speed? Looking at units is helpful.)

Answer 1