Math

CalculusQ&A LibraryFind 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 = $18.90I am a bit confused about this question and I ve done all the steps right but cant get the right answerQuestion

Asked Feb 14, 2019

958 views

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

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 = v^{2} / 240, W = 18.90 and T = 115 / v

Hence our total cost of the trip, TC(v) = CT + WT = v^{2} / 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...

Find answers to questions asked by student like you

Show more Q&A

Q: 4. Two stationary patrol cars equipped with radar are 6 miles apart on a highway. A truck passes a p...

A: Using Mean value theoremt,to calculate the speed limit of the truck driver passing the second patrol...

Q: :)

A: Given:The given curves are y = x2, x = 1, and y = 0.The volume of the solid revolved around the line...

Q: Help me please

A: The general Taylor series for sin x at x = 0 is as follows.

Q: What is Calculus

A: Refer to the question what is calculus,It is topic of maths which helps in studying curves, and find...

Q: How can I get the result? Which is the result?

A: We have to find limits.Question is given below:

Q: Find the function represented by the following series and find the interval of convergence of the se...

A: The function is given by,

Q: Use the derivative f' to determine local minima and maxima of f and the intervals of increase and de...

A: When f'(x)>0 then f(x) is increasing. Answer: f(x) is increasing in (-4pi/3,-pi)U(-2pi/3,-pi/3)U(...

Q: If p 8m2-9m + 3, then the rate of change of p with respect to m when m 1 is 16. 1 -9, 7. 2.

A: Approach:A clear relationship between "p" and "m" is given"p" is dependent variable while "m" is the...

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by abo...

A: Click to see the answer