CUET · MATHS · PYQ PAPER 2023
consider the linear programming problem: Maximise \(z=3 x+y\) subject to the constraints \(x+y \leq 6, x \geq 0, y \geq 0\). Which of the following statements are true?
(A) \(x \geq 0, y \geq 0\) are non-negative restrictions.
(B) The point \((1,1)\) does not lie in the half plane \(x+y \leq 6\).
(C) There are 2 corner points of the feasible region of given LPP.
(D) Maximum value of \(z\) is 18.
Choose the correct answer from the options given below:
- A A and D only
- B \(A, B\) and \(C\) only
- C \(A, B\) and \(D\) only
- D A, B, C and D only
Answer & Solution
Correct Answer
(A) A and D only
Step-by-step Solution
Detailed explanation
(A) Non-negative restrictions for \(x \geq 0, y \geq 0\). True. (B) For \((1,1)\) in \(x+y \leq 6\): \(1+1 \leq 6 \Rightarrow 2 \leq 6\). Point lies in half plane. Statement is False. (C) Corner points of feasible region: \(x=0, y=0 \Rightarrow (0,0)\)…
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