Results 1 to 5 of 5

Math Help - Help needed setting up an inequalities word problem

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    6

    Help needed setting up an inequalities word problem

    I can't seem to figure out how to set this problem up. I can probably solve it, but I can't get anywhere unless I can set it up. The question is as follows...


    Suppose a TV dealer has stores in Annapolis and Rockville, and warehouses in College Park and Baltimore. The cost of shipping sets from College Park to Annapolis is $6 per set; from College Park to Rockville, $3; from Baltimore to Annapolis, $9; and from Baltimore to Rockville, $5. Suppose Annapolis store orders 25 sets and the Rockville store orders 30. Also, suppose that the College Park warehouse has 45 sets in stock, and that the Baltimore warehouse has 40 sets. What is the most economical way to ship the requested TV sets to the two stores, and what is the minimum cost?



    Let X1 = the number of sets shipped from College Park to Rockville.
    Let X2
    = the number of sets shipped from College Park to Annapolis.


    I know it's going to be an inequality set with mixed constraints because I have to solve using the Big M method. I appreciate any help that can be given. Thanks in advance
    Last edited by Videodrone; November 1st 2009 at 09:46 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Videodrone

    Welcome to Math Help Forum!
    Quote Originally Posted by Videodrone View Post
    I can't seem to figure out how to set this problem up. I can probably solve it, but I can't get anywhere unless I can set it up. The question is as follows...


    Suppose a TV dealer has stores in Annapolis and Rockville, and warehouses in College Park and Baltimore. The cost of shipping sets from College Park to Annapolis is $6 per set; from College Park to Rockville, $3; from Baltimore to Annapolis, $9; and from Baltimore to Rockville, $5. Suppose Annapolis store orders 25 sets and the Rockville store orders 30. Also, suppose that the College Park warehouse has 45 sets in stock, and that the Baltimore warehouse has 40 sets. What is the most economical way to ship the requested TV sets to the two stores, and what is the minimum cost?



    Let X1 = the number of sets shipped from College Park to Rockville.
    Let X2
    = the number of sets shipped from College Park to Annapolis.


    I know it's going to be an inequality set with mixed constraints because I have to solve using the Big M method. I appreciate any help that can be given. Thanks in advance
    You have set this out beautifully. All you need to do now is to write down the various constraints and the total cost. Then minimise the cost.

    College Park has 45 in stock. So
    x_1+x_2\le45
    Baltimore has 40 in stock. So
    (30-x_1) + (25-x_2)\le40 (which you can simplify)
    And the total cost, $ C, is:
    C = 3x_1+6x_2 + 5(30-x_1)+9(25-x_2) (which also can be simplified)
    Can you take it from here?

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    6
    Awesome. I think I can go from here. If not I will be back! I really appreciate the help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    6
    Ok so now I have a new problem. When I simplified for C i got...


    C = -2x_1 - 3x_2 + 375


    What do I do with that 375? Did i simplify it wrong?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Videodrone
    Quote Originally Posted by Videodrone View Post
    Ok so now I have a new problem. When I simplified for C i got...


    C = -2x_1 - 3x_2 + 375


    What do I do with that 375? Did i simplify it wrong?
    No, that's correct. You now have to minimise C, given that C=375-(2x_1+3x_2). So you'll need to maximise 2x_1+3x_2.

    (Never having used the Big M method, I should do it graphically, but perhaps you have been told to do it in a particular way.)

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trouble setting up derivative word problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 21st 2011, 08:35 PM
  2. Replies: 2
    Last Post: May 11th 2011, 05:54 AM
  3. Help needed setting up a word problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: December 4th 2009, 04:45 PM
  4. Inequalities help with word problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 11th 2009, 06:27 PM
  5. Inequalities Word Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 10th 2007, 08:00 PM

Search Tags


/mathhelpforum @mathhelpforum