My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 26th, 2013, 03:54 PM   #1
Member
 
Joined: Feb 2013

Posts: 44
Thanks: 0

2 questions in my math analysis hmw.

The management of the UNICO department store has decided to enclose a 906 ft² area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

So we use the equations they gave us. A = xy
P = 2x + y

I already set 906 = xy and solved for y. then plugged it into for P and solved for x. and that's where I got lost.



2, The demand for motorcycle tires imported by Dixie Import-Export is 49,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $360, and the cost of storing each tire for a year is $2. Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)

No idea what to do for this one.
hamburgertime is offline  
 
October 26th, 2013, 06:06 PM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,295
Thanks: 1686

The fencing (in $) costs 14x + 2y = 14x + 2A/x = (?(14x) - ?(2A/x))² + 2?(14)?(2A),
which is minimized when ?(14x) = ?(2A/x) (which requires x = ?(A/7), so y = A/x = ?(7A)).
The question gives the value of A.
skipjack is offline  
October 26th, 2013, 07:08 PM   #3
Member
 
Joined: Feb 2013

Posts: 44
Thanks: 0

Re: 2 questions in my math analysis hmw.

So what's the answer? None of that made any sense to me. lol
hamburgertime is offline  
October 26th, 2013, 09:43 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,193
Thanks: 504

Math Focus: Calculus/ODEs
Re: 2 questions in my math analysis hmw.

1.) [color=#BF0000]skipjack[/color] used a technique that does not require the calculus. If you let be the length of the two sides perpendicular to the wall and be the length of the side parallel to the wall (both in feet), then your cost function in dollars is:



We are constrained by the fact that the rectangular area is:



Hence:



And so we may express the cost function in terms of one variable x:



What you want to do now is equate the derivative to zero to find the critical value for x. You are probably expected to use either the first or second derivative tests to demonstrate that this critical value is a relative maximum.
MarkFL is online now  
October 27th, 2013, 03:37 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 19,295
Thanks: 1686

Using calculus, one first needs to find the critical point (there happens to be only one for x > 0), and then show that its a relative minimum. It's then easy to see that it's the absolute minimum as well.
skipjack is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
analysis, hmw, math, questions



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Two very basic questions related to time series analysis sydfremmer Advanced Statistics 1 December 17th, 2012 12:27 PM
Unit Analysis Questions Nevischio Algebra 1 December 13th, 2010 06:42 PM
Calculus/analysis sequences questions jason.spade Calculus 0 November 17th, 2010 08:53 AM
math analysis alice 9 Real Analysis 3 September 29th, 2010 05:17 PM
ANALYSIS QUESTIONS LINEAR/QUADRILATERAL peterle1 Algebra 3 February 6th, 2010 08:44 PM





Copyright © 2018 My Math Forum. All rights reserved.