Solve the following linear programming problem graphically: Maximise Z=2 x+3 y subject to the constraints:

On plotting the graph of x+y ≤ 6, x ≥ 2, y ≤ 3, & x ≥ 0, y ≥ 0 we get the following graph and common shaded region is the region ABCD. Now, Corner points of the common shaded region are A (2,3), B(3,3), C(6,0) & D(2,0).Thus, So, Maximum Value of Z is 15 at x=3, y=3.

CBSE 2024 · Region 4 · Set 1 · Q30 · 3 marks

Solve the following linear programming problem graphically : Maximise $\displaystyle \mathrm{Z}=2 x+3 y$ subject to the constraints: \[\begin{aligned} & x+y \leq 6 \\ & x \geq 2 \\ & y \leq 3 \\ & x, y \geq 0 \end{aligned} \]

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Corner points		Value of $\displaystyle \mathrm{Z}=2 x+3 y$
\cline { $\displaystyle 1$ - $\displaystyle 1$ } \cline { $\displaystyle 3$ - $\displaystyle 3$ } $\displaystyle \mathrm{~A}(2,3)$		$\displaystyle 13$
$\displaystyle B(3,3)$		$\displaystyle 15$
$\displaystyle C(6,0)$		$\displaystyle 12$
$\displaystyle D(2,0)$		$\displaystyle 4$

Solve the following linear programming problem graphically : Maximise $\displaystyle \mathrm{Z}=2 x+3 y$ subject to the constraints: \[\begin{aligned} & x+y \leq 6 \\ & x \geq 2 \\ & y \leq 3 \\ & x, y \geq 0 \end{aligned} \]

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