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Part CCSIR NET June 2024an-unbounded-variable-hidden-among-bounded-ones

An unbounded variable hidden among bounded ones

Consider the linear programming problem: max{x1+x2+x3x_{1} + x_{2} + x_{3}} subject to constraints x1+x2−x3≤1,x1+x3≤2,0≤x1≤1/2,x2≥0x_{1} + x_{2} - x_{3} \le 1, x_{1} + x_{3} \le 2, 0 \le x_{1} \le 1/2, x_{2} \ge 0, and 0≤x3≤10 \le x_{3} \le 1. Which of the following statements are true?

  1. A.The optimum value is 3✓ Correct
  2. B.The optimum value is 3/2
  3. C.(0, 2, 1) is an extreme point of the feasible region✓ Correct
  4. D.(1/2, 0, 1) is the optimal solution

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 hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

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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