The cost of fuel is running an engine is proportional to the square of the speed in km/h is ₹48 per hour when the speed is 16 kn/h.Other costs amount to ₹300 per hour.Find the most economical speed?
1 Answer
Explanation:
Don't know that currency symbol so the euro,
"The cost of fuel is running an engine is proportional to the square of the speed..."
#implies C = k v^2#
And:
# 48 \ (€)/(hr) harr k ( 16 (km)/(hr))^2 implies k = 3/16#
"Other costs amount to €300 per hour":
#implies C = 3/16 v^2 + 300#
But that equation is useless because it measures the cost per hour.
This silly example makes the point. If you are going to costoptimise a use of the car for 100hours, you may as well just sit in it and pay only the other costs. You will go nowhere but you are not paying for fuel.
For this optimisation to make any physical sense, it should focus on true fuel efficiency, ie the allin cost of travelling a given distance.
Note:
So with

#bar C = C/v# 
#bar C = 3/16 v + 300/v#
graph{y = 3/16 x + 300/x [5, 200, 5, 50]}
Optimising by differentiating wrt
#(d bar C)/(dv) = 3/16  300/v^2 = 0#