CBSE 2023 · Region 2 · Set 2 · Q29 · 3 marks

Solve the following linear programming problem graphically : \[\begin{array}{ll} \text { Maximize : } \mathrm{Z}=\mathrm{x}+2 \mathrm{y} & \\ \text { subject to constraints : } & \mathrm{x}+2 \mathrm{y} \geq 100, \\ & 2 \mathrm{x}-\mathrm{y} \leq 0, \\ & 2 \mathrm{x}+\mathrm{y} \leq 200, \\ & \mathrm{x} \geq 0, \mathrm{y} \geq 0 . \end{array} \]

Linear ProgrammingLinear Programming Problem and its Mathematical FormulationApplyshort_answermedium

Corner points	Value of Z
$\displaystyle \mathbf{A}(\mathbf{0 , 2 0 0})$	$\displaystyle \mathbf{4 0 0}($ Max $\displaystyle )$
$\displaystyle \mathbf{B}(\mathbf{0 , 5 0})$	$\displaystyle \mathbf{1 0 0}$
$\displaystyle \mathbf{C}(\mathbf{2 0 , 4 0})$	$\displaystyle \mathbf{1 0 0}$
$\displaystyle \mathbf{D}(\mathbf{5 0 , 1 0 0})$	$\displaystyle \mathbf{2 5 0}$

Marking-scheme solution