CBSE 2025 · Region 5 · Set 1 · Q29 · 3 marks
In the Linear Programming Problem (LPP), find the point/points giving maximum value for $\displaystyle \mathrm{Z}=5 \mathrm{x}+10 \mathrm{y}$ subject to constraints \[\begin{aligned} & \mathrm{x}+2 \mathrm{y} \leq 120 \\ & \mathrm{x}+\mathrm{y} \geq 60 \\ & \mathrm{x}-2 \mathrm{y} \geq 0 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
The corner points of the feasible region are \(\displaystyle (60,0)\), \(\displaystyle (120,0)\), \(\displaystyle (60,30)\) and \(\displaystyle (40,20)\). Evaluating \(\displaystyle Z=5x+10y\):
\[\begin{array}{ll}
(60,0): & Z=300 \\
(120,0): & Z=600 \\
(60,30): & Z=600 \\
(40,20): & Z=400
\end{array}
\]
Maximum value \(\displaystyle Z=600\), attained at \(\displaystyle (120,0)\) and \(\displaystyle (60,30)\) — hence at every point on the line segment joining them.
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