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Math Help - Linear Programming Help

  1. #1
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    Sep 2012
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    South Africa
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    Linear Programming Help

    This is my first example of linear programming with ratios and I'm not really sure what to do. I need help finding the constraints and then I can work the rest out myself.

    Here's the question:
    The owner of a factory that manufactures kitchen units has a contract to supply at least 72 units per week.
    *He employs x artisans and y apprentices
    *He cannot accommodate more than 16 employees.
    *The Apprentices Act states that the ratio of apprentice to artisans is not greater than 9:2
    *The Trade Union Act rules require that the ratio of apprentices to artisans is not smaller than 1:2.
    *An artisan can produce 9 units per week while an apprentice can produce 6 units per week.

    1. Write down a system of inequalities to represent the information above.

    I can do the rest of the questions myself, just need to know the constraints.
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  2. #2
    Newbie
    Joined
    Dec 2012
    From
    United States
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    Re: Linear Programming Help

    The solution should be similar to what you see below, provided I did not make any mistakes.


    Let x be the number of artisans and y the number of apprentices.

    0 <= x + y <= 16 (he cannot accommodate more than 16 employees - note that you cannot have -1 employees, hence the greater than or equal to zero )

    1/2<y/x<9/2 (ratios of apprentices to artisans).

    Now, for the number of units,

    0<= 9x + 6y <= 72 (an artisan produces 9 units while an apprentice produces 6)
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