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Math Help - Big M method help

  1. #1
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    Big M method help

    I'm reading the textbook and trying to learn the material before the class starts. I'm stuck on the Big M method and it has me confused. The problem I'm currently working on is:

    Maximize: Z = 3x + 6y
    subject to:
    +2x + 2y ≤ 16 (if it's not displaying on your computer, thats a <=)
    +1x ≥ 4 (this is a >=)

    both x ≥ 0 and y ≥ 0

    the first part asks to find the initial objective function using the Big M method, then solve for the objective function you will use for the initial simplex tableau.

    The second part of the problem asks to find the optimal value for z using the tableau that is provided.

    Thanks.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by spoord View Post
    I'm reading the textbook and trying to learn the material before the class starts. I'm stuck on the Big M method and it has me confused. The problem I'm currently working on is:

    Maximize: Z = 3x + 6y
    subject to:
    +2x + 2y ≤ 16 (if it's not displaying on your computer, thats a <=)
    +1x ≥ 4 (this is a >=)

    both x ≥ 0 and y ≥ 0

    the first part asks to find the initial objective function using the Big M method, then solve for the objective function you will use for the initial simplex tableau.

    The second part of the problem asks to find the optimal value for z using the tableau that is provided.

    Thanks.
    I have no idea what is meant by the "big M" method but isn't your objective function just what you say- 3x+ 6y?
    Also, I am no expert on the simplex method so I would solve it graphically:
    2x+ 2y= 16 is the same as x+ y= 8 and its graph is the straight line from (0, 8) to (8, 0). The set of points such that 2x+ 2y\le 16 and [tex]x\ge 0[tex], y\ge 0 is triangle below that line, above y= 0 and to the right of x= 0.
    x= 4 is the vertical line through, say, (4, 0) and (4, 1) and x\ge 4 is to the right of that. That vertical line intersects the y-axis at (4, 0) and intersect the line x+ y= 8 at (4, 4). The "feasible" region, the region satisfying all inequalities is the triangle with vertices (4, 0), (4, 4), and (8, 0). The "fundamental theorem" of linear programming is that a linear function takes on its maximum and minimum values on a convex polygon at one of the vertices. Just evaluate z= 3x+ 6y at each of (4, 0), (4, 4), and (8, 0) to see which is 'optimum'.
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