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Part BCSIR NET December 2025check-every-vertex-the-optimum-need-not-sit-where-the-loosest-looking-constraint-binds

Check every vertex the optimum need not sit where the loosest looking constraint binds

Consider the following linear programming problem: Maximize 3x1+4x23x_{1} + 4x_{2} subject to 3x1+2x2≤12,3x1+5x2≤15,2x1−x2≥0,x2≤23x_{1} + 2x_{2} \le 12, 3x_{1} + 5x_{2} \le 15, 2x_{1} - x_{2} \ge 0, x_{2} \le 2, and x1,x2≥0x_{1}, x_{2} \ge 0. Which of the following values is the optimum value of the objective function in the feasible region?

  1. A.11
  2. B.13
  3. C.14✓ Correct
  4. D.15

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

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More on this topic

The chapter behind this: Linear programming, simplex and duality — free to read

From Linear Programming › Linear programming, simplex and duality

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