16. Given the following information, determine the constant speed, travel time, and cost

Question

that represent the minimum one-way trip delivery cost.

Fuel costs per hour are equal to V^2/600
V is the speed in miles per hour
Driver (labor) costs are $10 per hour
One-way distance is 110 miles

Answer 1

now express everything in terms of a single variable, say speed:
cost = time*wages + time*fuelcost
The time spent is distance/speed = 110/v

c = 110/v * 10 + 110/v * v^2/600
c = 1100/v + 11v/60

dc/dv = 11/60 - 1100/v^2
=11/60v^2 (v^2 - 6000)
dc/dv=0 when v=10√60 = 77.46

Seems kinda fast, but if you find my algebra ok, then

v = 77.46 mph
t = 110/77.46 = 1.42 hr
c = $28.40

Answer 2

thank you!!!