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Math Help - Linear programming problem

  1. #1
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    Linear programming problem

    Would very much appreciate some assistance with a Linear modelling problem. Facts: 2 production lines, 2 products, 8 hours per line (480 min), profit for each product, a is $42, b is $87

    Line 1 Line 2
    Product a 3 minutes 4 min
    Product b 6 minutes 2 min

    Maximize profit formula: 42a + 87b
    Constraints: 3a + 6b<=480
    4a + 2b<=480

    I'm trying to determine the additional constraint that reflects the question...
    how can we limit the difference between the total time on line 1 and the total time on line 2 to 30 minutes or less...in order to maximize profit? Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Stormy-1 View Post
    Would very much appreciate some assistance with a Linear modelling problem. Facts: 2 production lines, 2 products, 8 hours per line (480 min), profit for each product, a is $42, b is $87

    Line 1 Line 2
    Product a 3 minutes 4 min
    Product b 6 minutes 2 min

    Maximize profit formula: 42a + 87b
    Constraints: 3a + 6b<=480
    4a + 2b<=480

    I'm trying to determine the additional constraint that reflects the question...
    how can we limit the difference between the total time on line 1 and the total time on line 2 to 30 minutes or less...in order to maximize profit? Thanks.
    Time on line 1 is t_1=3a+6b, time on line 2 is t_2=4a+2b

    So you want t_1-t_2=-a+4b \le 30 (and if its the a the absolute difference you want to limit you need t_2-t_1=a-4b \le 30 as well)

    RonL
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