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Which of the following is incorrect about the Linear Programming Problem (LPP)? |
If the feasible region R of a Linear Programming Problem (LPP) is bounded, then the objective function has both a maximum and a minimum value in R. An LPP can have no solution or more than one optimal solution. If two corner points of the feasible region are both optimal solutions of the same type, then any point on the line segment joining these two points is also an optimal solution of the same type. If the feasible region is unbounded, then a minimum value of the objective function always exists. |
If the feasible region is unbounded, then a minimum value of the objective function always exists. |
The correct answer is Option (4) → If the feasible region is unbounded, then a minimum value of the objective function always exists. Check each statement: (A) If feasible region is bounded, objective function has both maximum and minimum. This is true. (B) An LPP can have no solution or more than one optimal solution. This is true. (C) If two corner points are optimal, then every point on the line joining them is also optimal. This is true. (D) If feasible region is unbounded, then a minimum value always exists. This is false because in an unbounded region the objective function may decrease indefinitely. Incorrect statement is (D) |
