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Math Help - Solve the linear programming problem

  1. #1
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    Solve the linear programming problem

    Assume  x >= 0 and y >= 0

    Minimize C=4x+2y with the constraints.

    { x+y>=7, 4x+3y>=4, x<=10, y<=10 }

    So, the minimum is 10, now what ! lol
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  2. #2
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    Quote Originally Posted by RBlax View Post
    Assume  x >= 0 and y >= 0

    Minimize C=4x+2y with the constraints.

    { x+y>=7, 4x+3y>=4, x<=10, y<=10 }

    So, the minimum is 10, now what ! lol
    1. Re-write the equations (if possible) such that the y-variable is at the LHS of the inequality:

    x\geq0~\wedge~y\geq0

    y\geq -x+7~\wedge~y\geq-\frac43 x + \frac43~\wedge~x\leq10~\wedge~y\leq10

    2. Draw the corresponding lines which are the borders of the feasible region.

    3. The line y=-2x+\frac12 C must contain at least one point of the feasible region and the value of C must be a minimum.

    4. According to the sketch you see that

    7=\frac12 C ~\implies~C = 14

    5. To get an exact result calculate the coordinates of the vertices of the feasible region and check which vertex produces the minimum value of C.
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