CBSE 2025 · Region 6 · Set 1 · Q29 · 3 marks
Consider the Linear Programming Problem, where the objective function $\displaystyle \mathrm{Z}=(\mathrm{x}+4 \mathrm{y})$ needs to be minimized subject to constraints \[\begin{aligned} & 2 \mathrm{x}+\mathrm{y} \geq 1000 \\ & \mathrm{x}+2 \mathrm{y} \geq 800 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \] Draw a neat graph of the feasible region and find the minimum value of Z.
Marking-scheme solution
| Corner points | Value of Z |
| $\displaystyle (800, 0)$ | $\displaystyle 800$ minimum |
| $\displaystyle (400, 200)$ | $\displaystyle 1200$ |
| $\displaystyle (0, 1000)$ | $\displaystyle 4000$ |
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.