Question:
The maximum value of \(Z=x-3y\) subject to \(x+y\le13,\ x\ge0,\ y\ge0\) is
The maximum value of \(Z=x-3y\) subject to \(x+y\le13,\ x\ge0,\ y\ge0\) is
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Negative coefficient $\to$ push that variable to its minimum (if allowed).
Updated On: Oct 17, 2025
- \(39\)
- \(26\)
- \(13\)
- \(-26\)
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The Correct Option is C
Solution and Explanation
Since \(y\) has a negative coefficient in \(Z\), we want the smallest \(y\) (take \(y=0\)) and the largest \(x\) allowed.
With \(y=0\), the constraint becomes \(x\le13\).
Corner checks:
\((13,0)\Rightarrow Z=13\) (best), \((0,13)\Rightarrow Z=-39\), \((0,0)\Rightarrow Z=0\).
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