Consider a corner point to a linear programming problem, which lies at the intersection of the following two constraints:
6X₁ + 15X₂ ≤ 390
2X₁ + X₂ ≤ 50
Which of the following statements about the corner point is True?
A) X₁ ≤ 21
B) X₁ ≥ 25
C) X₁ ≤ 10
D) X₁ ≥ 17

Question

Consider a corner point to a linear programming problem, which lies at the intersection of the following two constraints: 
6X₁ + 15X₂ ≤ 390
2X₁ + X₂ ≤ 50
Which of the following statements about the corner point is True?
A) X₁ ≤ 21
B) X₁ ≥ 25
C) X₁ ≤ 10
D) X₁ ≥ 17

Quizplus · Accepted Answer

The corner point lies at the intersection of the two constraints, so it satisfies both constraints as equalities. Substituting X₂ = 50 - 2X₁ into the first constraint, we get 6X₁ + 15(50 - 2X₁) = 390, which simplifies to X₁ = 21. Therefore, X₁ ≤ 21.

Consider a Corner Point to a Linear Programming Problem, Which