A truck has a minimum speed of 10 mph in high gear. When traveling x mph, the tr

Question

A truck has a minimum speed of 10 mph in high gear. When traveling x mph, the truck burns diesel fuel at the rate of

Assuming that the truck can not be driven over 56 mph and that diesel fuel costs $1.44 a gallon, find the following.

(a) The steady speed that will minimize the cost of the fuel for a 450 mile trip.
x=

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

(c) The steady speed that will minimize the total cost of a 560 mile trip if the driver is paid $22 an hour.
x=

i got a and b

plz solve (c)

(dont say "solve like (b)" )

Explanation / Answer

(c) we have to minimise f(x) =   0.0061781(1089x+x^2)*560*1.44 + 560*22/x

for minima , f'(x) =0

or,

0 = 0.0061781(1089 +2x)*560 *1.44 - 560*22 / x^2

on solving , we get x= 60

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