Question:
The maximum value of \(z = 3x + 2y\) subject to \(x + 2y \ge 2\), \(x + 2y \le 8\), \(y \ge 0\) is
The maximum value of \(z = 3x + 2y\) subject to \(x + 2y \ge 2\), \(x + 2y \le 8\), \(y \ge 0\) is
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For linear programming, maxima occur at boundary points.
Updated On: Mar 23, 2026
- 32
- 24
- 40
- None of these
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The Correct Option is B
Solution and Explanation
On the boundary \(x + 2y = 8\):
\[ z = 3(8 - 2y) + 2y = 24 - 4y \le 24 \]
Maximum occurs at \(y = 0 \implies z = 24\).
\[ z = 3(8 - 2y) + 2y = 24 - 4y \le 24 \]
Maximum occurs at \(y = 0 \implies z = 24\).
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