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Subject:  Finite Math

Maximise 5x + 4y subject to linear constraints

Solve a two-variable linear program by the graphical method.

Answer max z = 46 at (6, 4)

Solution

  1. Objective max z = 5x + 4y
  2. Constraints x + 2y <= 14; 3x - y >= 0; x - y <= 2; x >= 0; y >= 0
  3. Method Find intersections of every pair of boundary lines, keep the feasible ones, evaluate z at each vertex.
  4. Feasible vertices V1 = (2, 6), z = 34; V2 = (6, 4), z = 46; V3 = (0, 0), z = 0; V4 = (2, 0), z = 10
  5. Optimum (max) (6, 4), z = 46

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