Question 1072659
2. Assume that the cost of fuel for a ship is proportional to the cube of velocity of the ship.
 When the velocity is 10 km/h the cost of fuel is $80 per hour, and other expenses for the ship are $480 per hour.
What velocity of the ship minimizes the total expenses if the ship sails 20km?
In this case what are the total expenses per hour?
:
Fuel cost equation
v^3*k = cost/hr
Using the given values
10^3*k = 80
1000k = 80
k = {{{80/1000}}}
k = .08
The hourly fuel cost expression = .08v^3
:
Cost equation for a 20 km 
C(v) = {{{20/v}}}(.08v^3 + 480)
graphically
{{{ graph( 300, 200, -6, 30, -200, 2000, (20/x)(.08x^3+480)) }}}
Minimum cost at a velocity of 14.4 km/hr
:
"In this case what are the total expenses per hour?"
.08(14.4^3) = $238.87 per hr
:
Cost for a 20 km trip
C(v) = {{{20/14.4}}}(.08*14.4^3 + 480)
C(v) = $998.44