A truck has a minimum speed of 14 mph in high gear. When traveling $x$ mph, the truck burns diesel fuel at the rate of $$0.0029847\left(\frac{729}{x}+x\right)\frac{\mbox{gal}}{\mbox{mile}}$$ Assuming that the truck can not be driven over 65 mph and that diesel fuel costs $1.69 a gallon, find the following.

(a) The steady speed that will minimize the cost of the fuel for a 420 mile trip.
$x=$

(b) The steady speed that will minimize the total cost of a 420 mile trip if the driver is paid $13 an hour.
$x=$

(c) The steady speed that will minimize the total cost of a 550 mile trip if the driver is paid $20 an hour.
$x=$