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CUET · MATHS · PYQ PAPER 2023

The function \(Z=\alpha x+\beta y(\alpha, \beta>0)\) corresponds to the objective function of an LPP that needs to be maximized subject to \(x+y \leq 1, x, y \geq 0\).
Then the set of optimal solutions is:

  1. A Empty set
  2. B \(\{(1,0)\}\) if \(\alpha<\beta\)
  3. C \(\{(0,1)\}\) if \(\alpha>\beta\)
  4. D \(\{(t, 1-t): t \in[0,1]\}\) if \(\alpha=\beta\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\{(t, 1-t): t \in[0,1]\}\) if \(\alpha=\beta\)

Step-by-step Solution

Detailed explanation

Feasible region vertices: \((0,0), (1,0), (0,1)\). Evaluate \(Z=\alpha x+\beta y\) at vertices: \(Z(0,0)=0\) \(Z(1,0)=\alpha\) \(Z(0,1)=\beta\) If \(\alpha=\beta\): \(Z=\alpha x+\alpha y = \alpha(x+y)\). To maximize \(Z\) for \(\alpha>0\), maximize \(x+y\) subject to…
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