Solve the following linear programming problem graphically: Minimize z=x+2 y subject to the constraints

Corner points Value of Z = x + 2y --- --- (0, 3) 6 → Minimum (6, 0) 6 → Minimum The half plane x + 2y < 6 has no point common with feasible region. Hence, minimum z = 6 at all points on line segment AB

CBSE 2023 · Region 3 · Set 3 · Q31 · 3 marks

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

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Corner points	Value of $\displaystyle Z = x + 2y$
$\displaystyle (0, 3)$	$\displaystyle 6 \rightarrow$ Minimum
$\displaystyle (6, 0)$	$\displaystyle 6 \rightarrow$ Minimum

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

Marking-scheme solution

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