Max Z = 3x1 +2x2 Subject to: 3x1 + 5x2 30  &...

Max Z = 3x1 +2x2
Subject to: 3x1 + 5x2 30
                  4x1 + 2x228
                  x18
                 x1, x20 and integer
The solution to the Linear programming relaxation is: x1= 5.714, x2 = 2.571.
What is the optimal value of z of this integerlinearprogramming problem?
Our book doesn't decribe this process....
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    Answers ( 1 )

    1. maélie perez
      maélie perez
      Graphical Solution
      Graph all your inequalities.
      Your objective function is z = 3x1 +2x2.
      Draw the line 3x1 + 2x2 = c such that itpasses through the optimal vertex. The coordinates of this pointwill give you the optimal solution, as you noted in yourpost.
      To get the integer solution ...
      The x1 and x2 coordinates must beinteger values, so plot points in the feasible region, near to theoptimal vertex, all points to have integer coordinates.
      Then whichever point is nearest to the line 3x1 +2x2 = c passing through the optimal vertex is theinteger optimal solution.

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