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B.3 Solve the following linear programming problem graphically: Maximize profit = X + 10Y Subject to: %3D 4X + 3Y < 36 2X + 4Y < 40 Y > 3 X, Y > 0 PX

B.3 Solve the following linear programming problem graphically: Maximize profit = X + 10Y Subject to: %3D 4X + 3Y < 36 2X + 4Y < 40 Y > 3 X, Y > 0 PX

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Problem B.3: Solving a Linear Programming Problem **Objective:** Maximize the profit given by the equation: \[ \text{Profit} = X + 10Y \] **Constraints:** 1. \( 4X + 3Y \leq 36 \) 2. \( 2X + 4Y \leq 40 \) 3. \( Y \geq 3 \) 4. \( X, Y \geq 0 \) ### Explanation: To solve this linear programming problem graphically, we need to: 1. Graph the constraints on a coordinate plane. 2. Identify the feasible region bounded by these constraints. 3. Determine the vertices of the feasible region. 4. Evaluate the objective function at each vertex to find the maximum value. **Note:** The feasible region is where all constraints overlap, and the maximum profit occurs at one of the vertices of this region. If needed, further visualization can involve drawing the lines represented by each inequality, shading the feasible area, and marking the critical points for evaluation.
Transcribed Image Text:### Problem B.3: Solving a Linear Programming Problem **Objective:** Maximize the profit given by the equation: \[ \text{Profit} = X + 10Y \] **Constraints:** 1. \( 4X + 3Y \leq 36 \) 2. \( 2X + 4Y \leq 40 \) 3. \( Y \geq 3 \) 4. \( X, Y \geq 0 \) ### Explanation: To solve this linear programming problem graphically, we need to: 1. Graph the constraints on a coordinate plane. 2. Identify the feasible region bounded by these constraints. 3. Determine the vertices of the feasible region. 4. Evaluate the objective function at each vertex to find the maximum value. **Note:** The feasible region is where all constraints overlap, and the maximum profit occurs at one of the vertices of this region. If needed, further visualization can involve drawing the lines represented by each inequality, shading the feasible area, and marking the critical points for evaluation.
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