"Published in Newark, California, USA"
The cost of fuel per hour for running a ship is proportional to the cube of the speed and is $27 per hour when the speed is 12 miles per hour. Other costs amount to $128 per hour regardless of the speed. Express the cost per mile as a function of the speed, and find the speed that makes this cost a minimum.
Solution:
The first thing that we have to do is to analyze the given word problem as follows
Let C = cost of fuel per hour
v = speed of a ship
From the word problem, "The cost of fuel per hour for running a ship is proportional to the cube of the speed", the working equation will be
If C = $27 per hour
v = 12 miles per hour
then the value of k will be
Therefore
From the word problem, "Other costs amount to $128 per hour regardless of the speed", the final working equation will be
To get the minimum cost of a fuel as a function of the speed, take the derivative of the above equation with respect to v as follows
Set dC/dv = 0 since we are getting the minimum cost of a fuel as follows
