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Mathematics · 2024 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2024 · Region 3 · Set 1 · Q30
Solve the following linear programming problem graphically: Maximise z =4 x +3 y, subject to the constraints x + y ≤ 800; 2 x + y ≤ 1000; x ≤ 400; x,…
Solve the following linear programming problem graphically: Maximise $\displaystyle \mathrm{z}=4 \mathrm{x}+3 \mathrm{y}$, subject to the constraints \[\begin{aligned} & \mathrm{x}+\mathrm{y} \leq 800 \\ & 2 \mathrm{x}+\mathrm{y} \leq 1000 \\ & \mathrm{x} \leq 400 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
| Corner Point | Value of $\displaystyle z = 4x + 3y$ |
| $\displaystyle O(0,0)$ | $\displaystyle 0$ |
| $\displaystyle A(400,0)$ | $\displaystyle 1600$ |
| $\displaystyle B(400,200)$ | $\displaystyle 2200$ |
| $\displaystyle C(200,600)$ | $\displaystyle 2600$ |
| $\displaystyle D(0,800)$ | $\displaystyle 2400$ |
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.