Question

The maximum value of \(Z=x-3y\) subject to \(x+y\le13,\ x\ge0,\ y\ge0\) is

• A. \(39\)
• B. \(26\)
• C. \(13\)
• D. \(-26\)

Hint:

Negative coefficient $\to$ push that variable to its minimum (if allowed).

Answer 1

The Correct Option is C

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), \((0,13)\Rightarrow Z=-39\), \((0,0)\Rightarrow Z=0\).