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Mathematics · 2026 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2026 · Region 1 · Set 1 · Q30
Solve the following linear programming problem graphically: Minimize Z =13x-15y Subject to constraints x+y ≤ 7; 2 x-3 y+6 ≥ 0; x ≥ 0, y ≥ 0
Solve the following linear programming problem graphically :
Minimize $\displaystyle \mathrm{Z}=13x-15y$
Subject to constraints \[\begin{aligned} & x+y \leq 7 \\ & 2 x-3 y+6 \geq 0 \\ & x \geq 0, y \geq 0 \end{aligned} \]
Official answer
Minimum value of Z = -$\displaystyle 15$, occurring at the point $\displaystyle (0,1)$
Marking-scheme solution
| Corner point | Value of $\displaystyle Z = 13x - 15y$ |
| $\displaystyle (0, 0)$ | $\displaystyle 0$ |
| $\displaystyle (7, 0)$ | $\displaystyle 91$ |
| $\displaystyle (3, 4)$ | $\displaystyle -21$ |
| $\displaystyle (0, 2)$ | $\displaystyle -30$ |
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.