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Math Help - Generating a Linear Programming problem

  1. #1
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    Generating a Linear Programming problem

    Thanks. It was an error in the question. Problem solved.
    Last edited by DooBeeDoo; November 9th 2007 at 09:00 AM.
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  2. #2
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    Hello, DooBeeDoo!

    I can't tell what the right-hand side values of the constraints are.
    They weren't given . . .
    And without them, we can't write the constraints (exactly).


    A company manufactures two products from three scarce resources.
    The net profits are 4 and 3, respectively.

    Each unit of Product 1 uses 2 units of Resource1, 1 unit of Resource 2, and 3 units of Resource 3.

    Each unit of Product 2 uses 3 units of Resource 1, 2 units of Resource 2, and 2 units of Resource 3.

    Let x = number of Product 1 to be produced: . x \:\geq\:0
    Let y = number of Product 2 to be produced: . y \:\geq \:0

    I assume they want us to maximize the Profit Function: . P \:=\:4x + 3y


    We have the following information:

    \begin{array}{cccccccccc}& & \text{Resource 1} &|& \text{Resource 2} &|& \text{Resource 3} &|& \text{Profit} &| \\ \hline \text{Product 1 }(x) &|& 2x &|& x &|& 3x &|& 4x & | \\ \text{Product 2 }(y) &|& 3y &|& 2y &|& 2y &|& 3y &| \\ \hline \text{Available} &|& T_1 &|& T_2 &|& T_3 &|& &| \end{array}


    If we were given T_1,\:T_2,\:T_3, we could write the inequalities:

    . . \begin{array}{ccc}x & \geq & 0 \\ y & \geq & 0 \\ 2x + 3y & \leq & T_1 \\ x + 2y & \leq & T_2 \\ 3x +2y & \leq & T_3 \end{array}

    and solve the problem . . .

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