SOLUTION: 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 fo
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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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
k = .08
The hourly fuel cost expression = .08v^3
:
Cost equation for a 20 km
C(v) = (.08v^3 + 480)
graphically
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) = (.08*14.4^3 + 480)
C(v) = $998.44
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