Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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answer is D

**Graph the Constant-Profit Lines and Identify Maximum Profit Points** *Objective:* Use a straightedge to identify the corner point(s) where the maximum profit occurs for the given objective function. **Graph Explanation:** - The graph displayed shows a coordinate plane with various points marked and shaded regions. - The objective function is represented as \( P = x + y \). - The feasible region, which is shaded in blue, is bounded by the lines and axes. - Key points are plotted on the graph: (3, 2), (5, 3), (8, 4), and (0, 12). - The line passing through these points represents constant-profit lines. **Options for Maximum Profit (Point 35):** A) Max \( P = 8 \) at \( x = 5 \) and \( y = 3 \) B) Max \( P = 9 \) at \( x = 9 \) and \( y = 0 \), at \( x = 8 \) and \( y = 4 \), and at every point on the line segment joining the preceding two points. C) Max \( P = 5 \) at \( x = 3 \) and \( y = 2 \) D) Max \( P = 12 \) at \( x = 0 \) and \( y = 12 \), at \( x = 8 \) and \( y = 4 \), and at every point on the line segment joining the preceding two points. **Task:** Select the word or phrase that best completes each statement or answers the question. *Provide an appropriate response.* - Maximizing the objective given in the function by finding the right combination of variables involves analyzing these line segments and points for optimal solutions within the constraints of the given problem.
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Transcribed Image Text:**Graph the Constant-Profit Lines and Identify Maximum Profit Points** *Objective:* Use a straightedge to identify the corner point(s) where the maximum profit occurs for the given objective function. **Graph Explanation:** - The graph displayed shows a coordinate plane with various points marked and shaded regions. - The objective function is represented as \( P = x + y \). - The feasible region, which is shaded in blue, is bounded by the lines and axes. - Key points are plotted on the graph: (3, 2), (5, 3), (8, 4), and (0, 12). - The line passing through these points represents constant-profit lines. **Options for Maximum Profit (Point 35):** A) Max \( P = 8 \) at \( x = 5 \) and \( y = 3 \) B) Max \( P = 9 \) at \( x = 9 \) and \( y = 0 \), at \( x = 8 \) and \( y = 4 \), and at every point on the line segment joining the preceding two points. C) Max \( P = 5 \) at \( x = 3 \) and \( y = 2 \) D) Max \( P = 12 \) at \( x = 0 \) and \( y = 12 \), at \( x = 8 \) and \( y = 4 \), and at every point on the line segment joining the preceding two points. **Task:** Select the word or phrase that best completes each statement or answers the question. *Provide an appropriate response.* - Maximizing the objective given in the function by finding the right combination of variables involves analyzing these line segments and points for optimal solutions within the constraints of the given problem.
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