CBSE 2025, Set 1

Question

In a Linear Programming Problem, the objective function $Z = 5x + 4y$ needs to be maximised under constraints $3x + y \leq 6$, $x \leq 1$, $x, y \geq 0$. Express the LPP on the graph, shade the feasible region and mark the corner points.

Edvaya · Accepted Answer

The correct answer is Subjective. **Constraints:** $3x + y \leq 6$, $x \leq 1$, $x \geq 0$, $y \geq 0$ **Boundary lines:** - $3x + y = 6$: passes through $(2, 0)$ and $(0, 6)$ - $x = 1$ (vertical line) **Corner points of the feasible region:** - $O(0, 0)$: intersection of axes - $A(1, 0)$: intersection of $x = 1$ and $y = 0$ - $B(1, 3)$: intersection of $x = 1$ and $3(1) + y = 6 \Rightarrow y = 3$ - $C(0, 6)$: intersection of $3x + y = 6$ and $x = 0$ **Evaluating $Z = 5x + 4y$ at each corner:** | Corner Point | $Z = 5x + 4y$ | |---|---| | $O(0,0)$ | $0$ | | $A(1,0)$ | $5$ | | $B(1,3)$ | $5 + 12 = 17$ | | $C(0,6)$ | $24$ | **Maximum value of $Z = 24$ at $C(0, 6)$.** The feasible region is the quadrilateral $OABC$, bounded and shaded on the graph.

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Mathematics > Vectors And Linear Programming > Linear Programming

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