Find the speed v, in miles per hour, that will minimize costs on a 115-mile delivery trip. The cost per hour for fuel is C dollars, and the driver is paid W dollars per hour. (Assume there are no costs other than wages and fuel. Round your answer to one decimal place.)
Fuel cost: C = (v^2/240)
Driver: W = $18.90
I am a bit confused about this question and I ve done all the steps right but cant get the right answer
Length of trip, L = 115 miles
If "v" is the velocity in miles per hour, time T taken to complete the trip = Length / velocity = L / v
There are two components of cost:
The cost per hour for fuel is C dollars,
and the driver is paid W dollars per hour.
Hence the cost for the entire trip = The cost per hour for fuel x total number of hours + Hourly cost driver x total number of hours
= C x T + W x T
C = v2 / 240, W = 18.90 and T = 115 / v
Hence our total cost of the trip, TC(v) = CT + WT = v2 / 240 x 115 / v + 18.90 x 115 / v = 23/48 x v + 2,173.50 / v
In order to minimise this total cost, we need to differentiate this with respect to v and equate it to zero.
Let's recall the famour rule of differentiation: d(xn) / dx = nxn-1
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