CUET · MATHS · PYQ PAPER 2023
If \(A, B\) and \(C\) are all the corner points of feasible region (bounded) of an LPP with objective function \(Z\) that needs to be maximized such that \(Z_A>Z_B\) and \(Z_C < Z_A\) (Here \(Z_A\) denotes value of \(Z\) at \(A\) ), then which of the following statements is TRUE ?
- A There are infinitely many optimal solutions
- B There are exactly two optimal solutions
- C There is a unique optimal solution
- D Optimal solution does not exist
Answer & Solution
Correct Answer
(C) There is a unique optimal solution
Step-by-step Solution
Detailed explanation
Given: \(Z_A > Z_B\) and \(Z_C Combining the inequalities, \(Z_A\) is the maximum value among \(Z_A, Z_B, Z_C\). Since \(Z_A\) is strictly greater than \(Z_B\) and \(Z_C\), the optimal solution is unique. There is a unique optimal solution
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