CBSE 2025 · Region 5 · Set 3 · Q19 · 1 mark
Assertion (A) : The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP).
$\displaystyle \operatorname{Min} \mathrm{Z}=50 \mathrm{x}+70 \mathrm{y}$ subject to constraints $\displaystyle 2 \mathrm{x}+\mathrm{y} \geq 8, \mathrm{x}+2 \mathrm{y} \geq 10, \mathrm{x}, \mathrm{y} \geq 0$ $\displaystyle \mathrm{Z}=50 \mathrm{x}+70 \mathrm{y}$ has a minimum value $\displaystyle =380$ at $\displaystyle \mathrm{B}(2,4)$.
Reason (R): The region representing $\displaystyle 50 \mathrm{x}+70 \mathrm{y}<380$ does not have any point common with the feasible region.
$\displaystyle \operatorname{Min} \mathrm{Z}=50 \mathrm{x}+70 \mathrm{y}$ subject to constraints $\displaystyle 2 \mathrm{x}+\mathrm{y} \geq 8, \mathrm{x}+2 \mathrm{y} \geq 10, \mathrm{x}, \mathrm{y} \geq 0$ $\displaystyle \mathrm{Z}=50 \mathrm{x}+70 \mathrm{y}$ has a minimum value $\displaystyle =380$ at $\displaystyle \mathrm{B}(2,4)$.
Reason (R): The region representing $\displaystyle 50 \mathrm{x}+70 \mathrm{y}<380$ does not have any point common with the feasible region.Official answer
From CBSE’s own marking scheme for this paper.
(A)
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Linear ProgrammingLinear Programming Problem and its Mathematical FormulationAnalyseassertion_reasonmedium
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.