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Math Help - Difficult Linear Programming Problem

  1. #1
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    Dec 2009
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    Difficult Linear Programming Problem

    A factory makes seven products (PROD 1 - PROD 7) on the following machines: three grinders, two vertical drills, three horizontal drills, one borer and one planer. Each product yields a certain contribution to profit (defined as /unit selling price minus cost of raw materials). These profit contributions (in /unit) together with the unit production times (hours) required on each process are given below. (A dash indicates a product does not require a process).

    (i cant do a table)
    but each column is PROD 1 - PROD 7 i.e 7 columns

    10 6 8 4 11 9 3 (contribution to profit)
    0.5 0.7 - - 0.3 0.2 0.5 (grinding)
    0.1 0.2 - 0.3 - 0.6 - (vertical drilling)
    0.2 - 0.8 - - - 0.6 (horizontal drilling)
    0.05 0.03 - 0.07 0.1 - 0.08 (boring)
    - - 0.01 - 0.05 - 0.05 (planing)

    There are upper limits to the amount of each product the market can absorb each month, and in January these limits are as follows:

    columns are PROD 1 - PROD 7
    500 1000 300 300 800 200 100 (January)

    The factory works a 6 day week with two shifts of 8 hours each day. (Assume the month of January consists of 24 working days.) No sequencing problems need to be considered. Formulate a linear programming problem for determining how much of each product should be made in the month of January, so as to maximize profit in that month.

    I am not looking for this to be solved, I just want to know how do I go about putting these figures into a linear programming problem with constraints.
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  2. #2
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    Joined
    Dec 2009
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    hehe, long time ago I've played with these things. Here is an initial try:

    max profit_p1+profit_p2+...+profit_p7
    profit_p1=p1*10;
    profit_p2=p1*6;
    ...
    profit_p7=p1*3;

    //Limit production quantities
    p1<=500;
    p2<=1000;
    ...
    p7<=100;

    //Production time: 8 hours* 24 days
    ptime=8*24;

    //Productions

    //Grinding
    p1*0.5+p2*0.7+p5*0.3+p6*0.2+p7*0.5<=ptime;
    //Vertical drilling
    p1*0.1+p2*0.2+p4*0.3+p6*0.6<=ptime
    ...


    Let me know whether this makes sense, or whether I overlooked something
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