Statement I: Every Linear Programming Problem has at least one optimal solution. Statement II: If a…
Statement I: Every Linear Programming Problem has at least one optimal solution.
Statement II: If a Linear Programming Problem has two optimal solutions, then it has infinitely many solutions.
Which of the statements is correct?
- aStatement I is true and Statement II is false.
- bStatement I is false and Statement II is true.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
AIWritten by AI - it can contain mistakes.
Correct option: b
(b) Statement I is false and Statement II is true.
Statement I is false because an LPP can be infeasible or have an unbounded feasible region with no optimal solution.
Statement II is true because if an objective function takes the same optimal value at two distinct points, every point on the line segment joining them also yields the same optimal value, resulting in infinitely many optimal solutions.
From ISC 2027 Specimen Mathematics Paper 1, question 1(xiv).