My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 3rd, 2012, 02:33 PM   #1
Senior Member
 
Joined: Feb 2012

Posts: 110
Thanks: 0

Maximum production

The average manufacturing cost per unit (in hundreds of dollars) for producing x units of a product is given by:

C prime(x)= 2x^3-42x^2+288x+12 x is greater than or equal to 1 and less than or equal to 5

At what production level will the average cost per unit be maximum?

Do I take the 1st and 2nd derivatives of this equation or do I just take the first?
tsl182forever8 is offline  
 
March 3rd, 2012, 05:28 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Maximum production

First, let's look at a plot of the function of the given interval:

[attachment=0:2v9icl33]avgcost.jpg[/attachment:2v9icl33]

Obviously the function has its maximum value at x = 5 since there appear to be no extrema on the given interval. Let's verify that:

" />

We see that indeed the function has no critical points on the given interval and also we see that the slope must be positive on that interval, so the maximum value must occur at the right endpoint of the interval, or x = 5.
Attached Images
File Type: jpg avgcost.jpg (9.8 KB, 73 views)
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
maximum, production



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Real-world production problem billymac00 Applied Math 5 December 10th, 2013 03:15 PM
Production/Inventory Decision Rules shaunclinton Applied Math 1 August 24th, 2013 10:37 AM
production level-maximizing profit tsl182forever8 Calculus 11 March 2nd, 2012 03:59 PM
Production Function catherine19 Economics 0 August 8th, 2011 05:28 AM
lineaar production functions 123 Linear Algebra 0 October 15th, 2009 04:39 PM





Copyright © 2018 My Math Forum. All rights reserved.