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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (Show Source):
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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%2F1000
k = .08
The hourly fuel cost expression = .08v^3
:
Cost equation for a 20 km
C(v) = 20%2Fv(.08v^3 + 480)
graphically
+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+2000%2C+%2820%2Fx%29%28.08x%5E3%2B480%29%29+
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%2F14.4(.08*14.4^3 + 480)
C(v) = $998.44