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Mathematics · 2023 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2023 · Region 2 · Set 1 · Q31
Solve the following linear programming problem graphically: Minimize: Z =5 x+10 y subject to constraints: x+2 y ≤ 120, x+ y ≥ 60, x-2 y ≥ 0, x ≥ 0, y…
Solve the following linear programming problem graphically : Minimize : $\displaystyle \mathrm{Z}=5 x+10 \mathrm{y}$ subject to constraints : $\displaystyle x+2 \mathrm{y} \leq 120, x+\mathrm{y} \geq 60, x-2 \mathrm{y} \geq 0$, \[x \geq 0, \quad \mathrm{y} \geq 0 \]
Marking-scheme solution
Correct graph
| Corner points | Value of Z |
| $\displaystyle \mathbf{A}(\mathbf{4 0 , 2 0})$ | $\displaystyle \mathbf{4 0 0}$ |
| $\displaystyle \mathbf{B}(\mathbf{6 0 , 3 0})$ | $\displaystyle \mathbf{6 0 0}$ |
| $\displaystyle \mathbf{C}(\mathbf{1 2 0 , 0})$ | $\displaystyle \mathbf{6 0 0}$ |
| $\displaystyle \mathbf{D}(\mathbf{6 0 , 0})$ | $\displaystyle \mathbf{3 0 0}(\mathbf{M i n})$ |
| $\displaystyle \mathbf{M i n}(\mathbf{Z})=\mathbf{3 0 0}$ at $\displaystyle \mathbf{x}=\mathbf{6 0} ; \mathbf{y}=\mathbf{0}$ |
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.