My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 12th, 2014, 07:12 PM   #1
Newbie
 
Joined: Dec 2014
From: San Diego

Posts: 1
Thanks: 0

Wink Can you help me find the number of automobiles that must be produced to minimize cost

O.K. so my math teacher says this is going to be on the final but we never did this so I don't know how to solve it:

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-32x+128. Find the automobiles that must be produced to minimize the cost.

The answer is 4(thousand) but I don't know what to do to get that answer. Does anyone know?
Numbermanipulator is offline  
 
December 12th, 2014, 07:55 PM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
To minimize a function, take the derivative and set it equal to zero. That, or one of the endpoints, should give the location of the minimum.
CRGreathouse is offline  
December 12th, 2014, 08:42 PM   #3
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,685
Thanks: 2665

Math Focus: Mainly analysis and algebra
$$\begin{align*}C(x)&=4x^2-32x+128 \\ &= 4(x^2 - 8x + 32) \\ &= 4\left((x-8x+16)+16\right) \\ &= 4\left((x-4)^2+16\right) \end{align*}$$
And now we see that the minimum value of $(x-4)^2$ is zero - attained when $x = 4$. So the minimum value of $C(x)$ must be $4 \times 16 = 64$, attained when $x = 4$.

This is called 'completing the square' or putting the equation into 'vertex form'.

Last edited by v8archie; December 12th, 2014 at 08:47 PM.
v8archie is offline  
December 13th, 2014, 03:31 PM   #4
Member
 
Joined: Sep 2014
From: Kansas

Posts: 34
Thanks: 1

Wow I must've actually learned something this semester I knew how to solve that. LOL.
badmathdog is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
automobiles, cost, find, minimize, number, produced



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find the loss or gain percent on the total cost price. Chikis Elementary Math 5 October 22nd, 2014 04:43 AM
Sequence produced by sieving Petek Number Theory 8 February 13th, 2014 09:34 PM
Finding all integers produced by a fraction Akcope Number Theory 4 October 4th, 2013 08:02 PM
Need help to find minimal cost to complete a task summoner Advanced Statistics 3 November 6th, 2012 04:08 PM





Copyright © 2019 My Math Forum. All rights reserved.