Question
Asked Feb 14, 2019
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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

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Expert Answer

Step 1

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.

Step 2

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.

Step 3

Let's recall the famour rule of differentiation: d(xn) / dx = nxn-1

Please...

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