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Mathematics · 2025 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2025 · Region 1 · Set 3 · Q26
Solve the following linear programming problem graphically: Maximize Z =8 x +9 y Subject to the constraints: 2 x +3 y ≤ 6; 3 x -2 y ≤ 6; y ≤ 1; x ≥…
Solve the following linear programming problem graphically : Maximize $\displaystyle \mathrm{Z}=8 \mathrm{x}+9 \mathrm{y}$ Subject to the constraints : \[\begin{aligned} & 2 \mathrm{x}+3 \mathrm{y} \leq 6 \\ & 3 \mathrm{x}-2 \mathrm{y} \leq 6 \\ & \mathrm{y} \leq 1 \\ & \mathrm{x} \geq 0, \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
| Corner Point | Value of $\displaystyle \mathrm{Z}=8 \mathrm{x}+9 \mathrm{y}$ |
| $\displaystyle A(0,1)$ | $\displaystyle 9$ |
| $\displaystyle B\left(\frac{3}{2}, 1\right)$ | $\displaystyle 21$ |
| $\displaystyle C\left(\frac{30}{13}, \frac{6}{13}\right)$ | $\displaystyle \frac{294}{13}$ |
| $\displaystyle D(2,0)$ | $\displaystyle 16$ |
| $\displaystyle O(0,0)$ | $\displaystyle 0$ |
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.