A truck has a minimum speed of 15 mph in high gear. When traveling x mph, the truck burns diesel fuel at the rate of

0.0110469 ( 1156/x + x) gal/mile.

Assuming that the truck can not be driven over 54 mph and that diesel fuel costs $1.21 a gallon, find the steady speed that will minimize the total cost of the trip if the driver is paid $20 an hour.

Question

A truck has a minimum speed of 15 mph in high gear. When traveling x mph, the truck burns diesel fuel at the rate of

0.0110469 ( 1156/x + x) gal/mile.

Assuming that the truck can not be driven over 54 mph and that diesel fuel costs $1.21 a gallon, find the steady speed that will minimize the total cost of the trip if the driver is paid $20 an hour.

anonymous · Answer

$$\delta y/\delta x (0.0110459 (1156/x+x)=0$$

the derivative is $$0.01101459(-1156/x^2+1)$$

then you just solve for x, which it would be 34 mpg

anonymous · Answer

that was the answer of another part of this question, which is : The steady speed that will minimize the cost of the fuel for a 620 mile trip

anonymous · Answer

oh srry, didnt see the other one

anonymous · Answer

that should be the right answer though, because it consumes the least about of gasoline