Question:
The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is
The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is
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In linear programming, the maximum or minimum value of the objective function occurs at one of the corner points of the feasible region.
Updated On: Mar 28, 2026
- 30
- 27
- 36
- 32
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The Correct Option is C
Solution and Explanation
Step 1: Set up the constraints.
We are given a set of linear constraints and we need to maximize the objective function \( z = 3x + 5y \). We first graph the constraints and identify the feasible region.
Step 2: Check the corner points.
The maximum value of \( z \) occurs at one of the corner points of the feasible region. After evaluating the objective function at each corner point, we find that the maximum value of \( z \) is 36.
Step 3: Conclusion.
Thus, the maximum value of \( z \) is 36, corresponding to option (C).
We are given a set of linear constraints and we need to maximize the objective function \( z = 3x + 5y \). We first graph the constraints and identify the feasible region.
Step 2: Check the corner points.
The maximum value of \( z \) occurs at one of the corner points of the feasible region. After evaluating the objective function at each corner point, we find that the maximum value of \( z \) is 36.
Step 3: Conclusion.
Thus, the maximum value of \( z \) is 36, corresponding to option (C).
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