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Linear Programming - 4 variables I think?

  • 29-01-2011 04:26PM
    #1
    Blondini
    Closed Accounts Posts: 1,480 ✭✭✭


    Hi all,

    Any experts on Linear Programming here. Have a wordy problem with I think 4 variables.

    Will type in details if anyone thinks they could help..

    Thanks in advance..:)


Comments

  • #2
    LeixlipRed
    Closed Accounts Posts: 6,081 ✭✭✭LeixlipRed


    Where's the question?


  • #3
    Blondini
    Closed Accounts Posts: 1,480 ✭✭✭Blondini


    Edited out original question until I get it clarified re missing info.

    Thanks for the input graduate!!


  • #4
    graduate
    Registered Users, Registered Users 2 Posts: 335 ✭✭graduate


    You don't have an constraints on the availability of workers. So clearly you just use the cheapest for each job, e.g. Brickies cost €35.71 for roofing so you would clearly use a roofer. Only if the availability of workers is constrained would you need to substitute one for the other, and need a linear program.


  • #5
    Blondini
    Closed Accounts Posts: 1,480 ✭✭✭Blondini


    graduate wrote: »
    You don't have an constraints on the availability of workers. So clearly you just use the cheapest for each job, e.g. Brickies cost €35.71 for roofing so you would clearly use a roofer. Only if the availability of workers is constrained would you need to substitute one for the other, and need a linear program.

    Maybe you have hit the nail on the head as to why I couldnt get started.

    If there were contraints what way I go about assigning variables ? and woud the object of the exercise be to minimise this: 400bricklaying+300roofing+200plumbing+1000generalwork

    Thanks for the help


  • #6
    graduate
    Registered Users, Registered Users 2 Posts: 335 ✭✭graduate


    You have 4 trades and 4 types of work. You could have up to 16 variables

    X11 = brickies bricklaying
    X12 = brickies roofing
    X21 = roofers bricklaying
    X22 = roofers roofing
    etc


    then your LP is

    MIN 25(x11+x12+ x13 +x14) + 30(x21+x22+ x23 + x24) .......

    subject to
    x11 + x21 +0.5x31 + 0.4x41 > 400 (do all the brickwork)
    x12 + x22 + 0.5x32 > (do all the roofing)
    ......
    and the missing constraints
    X11 + X12 + X13 + X14 < hours worked by blocklayers

    this makes sense to me!


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