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Math Help - Help with Linear programming problem

  1. #1
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    Post Help with Linear programming problem

    There are three types of machines that can be used to make a chemical. The chemical can be manufactured at four different purity levels. Here is the data.

    Machine Capacity: production per day
    Production per day if used to manufacture purity
    1 2 3 4
    1 50 tons $900 1000 1250 1500
    2 40 tons 600 750 1000 1050
    3 25 tons 400 700 800 900

    Monthly demand for chemical at
    purity level (tons) 150 300 90 175
    Penalty per ton short 40 60 75 90

    The chemical is used by the company internally; if the company does not manufacture enough of It, It can be bought at a price, which is called the penalty for shortage. Assume that there are 30 production days per month at the company. Formulate the problem of minimizing the overall cost as an LP.

    Can anyone help me find the Variables, Constraints and the objective??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Maxerazzi View Post
    There are three types of machines that can be used to make a chemical. The chemical can be manufactured at four different purity levels. Here is the data.

    Machine Capacity: production per day
    Production per day if used to manufacture purity
    1 2 3 4
    1 50 tons $900 1000 1250 1500
    2 40 tons 600 750 1000 1050
    3 25 tons 400 700 800 900

    Monthly demand for chemical at
    purity level (tons) 150 300 90 175
    Penalty per ton short 40 60 75 90

    The chemical is used by the company internally; if the company does not manufacture enough of It, It can be bought at a price, which is called the penalty for shortage. Assume that there are 30 production days per month at the company. Formulate the problem of minimizing the overall cost as an LP.

    Can anyone help me find the Variables, Constraints and the objective??
    The variables are X_{i,j} the number of days production by machine i of quality level j.

    With these variables tables give the constraints. The objective is the total cost of meeting the production quotas when the penalty costs for the short fall in company production is included.

    CB
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  3. #3
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    Well my Lp isn't that great, this is what i originally had as an answer:

    Variables: purity=P, machine=M

    P1M1, P1M2, P1M3
    P2M1, P2M2, P2M3
    P3M1, P3M2, P3M3
    P4M1, P4M2, P4M3

    Objective:

    MINIMIZE; 900 P1M1 + 1000 P2M1 + 1250 P3M1
    + 1500 P4M1 + 600 P1M2 + ......... 900 P4M3.


    Constraints:

    demand purity level;

    Demand1 : P1M1+P1M2+P1M3 >= 150
    D2 : P2M1+P2M2+P2M3 >= 300
    D3 : P3M1+P3M2+P3M3 >= 90
    D4 : P4M1+P4M2+P4M3 >= 175



    This is what I had so far. Is some correct or is it totally wrong?
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