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Mathematics · 2023 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2023 · Region 3 · Set 1 · Q30
Determine graphically the minimum value of the following objective function: z =500 x +400 y subject to constraints; x + y ≤ 200; x ≥ 20; y ≥ 4 x; y…
Determine graphically the minimum value of the following objective function : \[\begin{aligned} & \mathrm{z}=500 \mathrm{x}+400 \mathrm{y} \\ & \quad \text { subject to constraints } \\ & \mathrm{x}+\mathrm{y} \leq 200 \\ & \mathrm{x} \geq 20 \\ & \mathrm{y} \geq 4 \mathrm{x} \\ & \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
Corner points
Value of $\displaystyle \mathrm{Z}=500 \mathrm{x}+400 \mathrm{y}$
$\displaystyle 82000$
$\displaystyle 84000$
$\displaystyle 42000 \rightarrow$ Minimum
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