Corner Point Calculator

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Choose whether to find the maximum or minimum value of the objective function.
The number multiplying x in P = px·x + py·y.
The number multiplying y in P = px·x + py·y.
Most real-world linear programs require x and y to be non-negative. Toggle off to allow negative values.
Choose how many structural constraints to enter (non-negativity bounds are separate).
Optimal P valueBounded feasible region
23

The maximum or minimum value of the objective function over the feasible region.

Optimal x3
Optimal y2
Number of corner points4
All corner points(0, 0) -> P = 0; (0, 3.5) -> P = 14; (4, 0) -> P = 20; (3, 2) -> P = 23

Maximum P = 23 at (3, 2)

  • The feasible region has 4 corner points. The corner point theorem guarantees the optimal value of any linear objective function always occurs at a vertex of the bounded feasible region.
  • At the optimal corner point (3, 2), the objective function gives P = 5x + 4y = 23.
  • Check the other 3 corner points in the "All corner points" output to verify no vertex gives a better value.

Next stepTo solve graphically, plot each constraint boundary line, shade the feasible side, identify all intersection points, then substitute each into P. This calculator does all three steps automatically.

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