fuel cost = miles * gal/mile * cost/gal
c(x) = 600 * 0.0086584(900/x +x) * 1.21 = 6.286 (x + 900/x)
dc/dx = 6.286 - 56.57.4/x^2
so minimum cost is when x = 30 mi/hr
time = distance/speed, so the total cost is
c(x) = 6.286 (x + 900/x) + 20*600/x = 6.286x + 17657.4/x
dc/dx = 6.286 - 17657.4/x^2
so minimum total cost is when x = 53 mi/hr
now adjust that c(x) for the new miles and cost
Pay attention to the domain of c(x)
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
0.0086584(900/x +x) gal/mile
Assuming that the truck can not be driven over 59 mph and that diesel fuel costs $1.21 a gallon, find the following.
a) The steady speed that will minimize the cost of the fuel for a 600 mile trip.
b) The steady speed that will minimize the total cost of a 600 mile trip if the driver is paid $20 an hour.
c) The steady speed that will minimize the total cost of a 520 mile trip if the driver is paid $31 an hour.
1 answer
1 answer