Question:
Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
Minimize Z = 5x + 3y \text{ subject to the constraints} \[ 4x + y \geq 80, \quad x + 5y \geq 115, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]
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In linear programming, the optimal solution occurs at one of the corner points of the feasible region.
Updated On: Mar 2, 2025
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Solution and Explanation
Step 1: Graph the constraints to form the feasible region.
Step 2: The objective function is \( Z = 5x + 3y \). Find the corner points of the feasible region.
Step 3: Evaluate \( Z \) at each corner point.
Step 4: Choose the corner point that gives the minimum value of \( Z \).
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