Question:medium
In a linear programming problem, the feasible region representing the maximization of the objective function \( Z = px + qy \), where \( p, q > 0 \), is a shaded polygonal region. If all points on the line segment joining the corner points \( A(0, 3) \) and \( B(3, 2) \) give the maximum value of \( Z \), then which of the following is true?
In a linear programming problem, the feasible region representing the maximization of the objective function \( Z = px + qy \), where \( p, q > 0 \), is a shaded polygonal region. If all points on the line segment joining the corner points \( A(0, 3) \) and \( B(3, 2) \) give the maximum value of \( Z \), then which of the following is true?
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When an objective function \(Z = px + qy\) achieves its maximum along an entire edge segment \(AB\), the slope of the objective function line must equal the slope of that boundary line segment \(AB\).
\[
\text{Slope of } Z \text{ line} = -\frac{p}{q}, \quad \text{Slope of } AB = \frac{2 - 3}{3 - 0} = -\frac{1}{3} \implies -\frac{p}{q} = -\frac{1}{3} \implies q = 3p
\]
Updated On: Jul 8, 2026
- \(p = 2q\)
- \(p = 3q\)
- \(q = 3p\)
- \(q = 2p\)
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The Correct Option is C
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