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Math Help - help linear programming

  1. #1
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    help linear programming

    Find minimum and maximum for these,objective
    1.C = 10x + 7y,constraints:0<=x<=60,0<=y<=45,5x+6y<=420;
    2.C=4x+6y,constraints:-x+y<=11,x+y<=27,2x+5y<=90;
    3.C=4x+3y,constraints:x=>0,2x+3y=>6,3x-2y<=9,x+5y<=20
    4.C=10x+3y,contraints:x=>0,Y=>0,-x+y=>0,2x+y=>4,2x+y<=13 using Linear programing(optimization)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zasi View Post
    Find minimum and maximum for these,objective
    1.C = 10x + 7y,constraints:0<=x<=60,0<=y<=45,5x+6y<=420;
    2.C=4x+6y,constraints:-x+y<=11,x+y<=27,2x+5y<=90;
    3.C=4x+3y,constraints:x=>0,2x+3y=>6,3x-2y<=9,x+5y<=20
    4.C=10x+3y,contraints:x=>0,Y=>0,-x+y=>0,2x+y=>4,2x+y<=13 using Linear programing(optimization)
    Now these are all essentialy the same so I will do the first one and leave
    the rest to you.

    First sketch the feasible region defined by the constraints (see attachment).

    The objective function takes its maximum and minimum at one of the
    corners or vetices of the feasible region, so we evaluate it at each
    at the maximum value it takes is the maximum on the feasible region,
    and similarly the minimum value at a vertex in the minimum on the feasible
    region.

    The vertices are (0,45), (30,45), (60,20), (60,0), (0,0), and the objective
    takes values : 315, 615, 740, 600, 0.

    So the maximum value of the objective is 740, which is achieved at (60,20),
    and the minimum is 0, which is achived at (0,0).

    RonL
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