Results 1 to 2 of 2

Math Help - linear programming

  1. #1
    Junior Member
    Joined
    Oct 2006
    Posts
    71

    linear programming

    question::A manufacturer of ovens must ship atleast 100industrial ovens to its west coast warehouses.Each warehouse holds a maximum of 100 ovens.
    warehouse A already has 25 ovens in storage and warehouse B has 20.Itcost $12 to ship an oven to warehouse a and $10 to ship one to warehouse B.union rule requires that atleast 300 workers ahould be hired.shippinh an oven to warehouse A requires 4 workers,while shipping oneto warehouse B requires 2 workers
    (a) how many ovens should be shipped to each warehouse to minimize cost
    (b)what is minimum cost
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by gracy View Post
    question::A manufacturer of ovens must ship atleast 100industrial ovens to its west coast warehouses.Each warehouse holds a maximum of 100 ovens.
    warehouse A already has 25 ovens in storage and warehouse B has 20.Itcost $12 to ship an oven to warehouse a and $10 to ship one to warehouse B.union rule requires that atleast 300 workers ahould be hired.shippinh an oven to warehouse A requires 4 workers,while shipping oneto warehouse B requires 2 workers
    (a) how many ovens should be shipped to each warehouse to minimize cost
    (b)what is minimum cost
    Hello,

    number of ovens shipped to A: x
    number of ovens shipped to B: y

    Then you can extract the following inequalities from your problem (I've copied the corresponding text from your problem):
    x+y\leq 100\ \Longrightarrow\ y\leq-x+100 ...A manufacturer of ovens must ship atleast 100industrial ovens...(black line)
    0\leq x\leq75 ...warehouse A already has 25 ovens...(green line)
    0 \leq y\leq80 ...warehouse B has 20...(green line)
    4x+2y\leq 300\ \Longrightarrow \ y\leq -2x+150 ...union rule requires that atleast 300 workers ahould be hired.shippinh an oven to warehouse A requires 4 workers,while shipping oneto warehouse B requires 2 workers...(blue line)

    I've sketched these inequalities. They form the circumference of the grey area.

    The costs of the shipping can be described by the function:
    c = 12x+10y\ \Longrightarrow\ y=-\frac{6}{5}x+\frac{c}{10}

    To minimize the costs the y-intercept of this line must be small. You'll get the best result if you ship 20 ovens to A and 80 ovens to B. Then the costs will be 1,040 $. I've sketched the optimal cost function (red line)

    To calculate the minimal costs plug in x = 20 and y = 80 into c = 12x+10y

    EB
    Attached Thumbnails Attached Thumbnails linear programming-oven_shipping.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Programming~Please help!
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: April 13th 2010, 01:12 PM
  2. Replies: 1
    Last Post: November 17th 2008, 03:18 AM
  3. linear programming
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 25th 2008, 03:59 PM
  4. linear programming
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 25th 2008, 06:40 AM
  5. Linear Programming
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: February 19th 2008, 07:06 AM

Search Tags


/mathhelpforum @mathhelpforum