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📐 Mathematics  ·  Linear Inequalities  ·  JEE

A company makes two products. Constraints from a related LP setup give x >= 0, y >= 0, x + 2y <= 10, and 2x + y <= 10. Which of these is NOT a corner point of the feasible region?

Answer: (10, 10).

  • A (0, 0)
  • B (5, 0)
  • C (10, 10)
  • D (10/3, 10/3)

Correct answer: C. (10, 10)

Explanation: (10,10) violates x + 2y <= 10 since 10 + 20 = 30 is far greater than 10, so it lies well outside the feasible region. The true corners are (0,0), (5,0), (0,5), and the intersection (10/3, 10/3).

Number Line vs Half-Plane Representationx > 2 (open circle, hollow)2x ≤ 2 (closed circle, filled)shaded regionsatisfies the inequality2D inequality: dashed line = strict, shaded = solution side

One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.

Concept context

Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.

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