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aph the constant-cost lines for the objective function C = 3x + 4 y ough (6,6) and also through (9,9). Use a straightedge to identify e corner point where the minimum cost occurs. Confirm your swer by constructing a corner point table. 15+ 10- 5- (0.15) (0,11) (3,4) T Fin (9.9) (6.6) 10 (15,15) (15,0) Q C Which graph below has the correct constant-cost line O A. B. 154 10- 5- O C. 15+ 10- 65 5 10 15 Q M 37 15- 10-1 5- O D. 154 10- 5 10 15

aph the constant-cost lines for the objective function C = 3x + 4 y ough (6,6) and also through (9,9). Use a straightedge to identify e corner point where the minimum cost occurs. Confirm your swer by constructing a corner point table. 15+ 10- 5- (0.15) (0,11) (3,4) T Fin (9.9) (6.6) 10 (15,15) (15,0) Q C Which graph below has the correct constant-cost line O A. B. 154 10- 5- O C. 15+ 10- 65 5 10 15 Q M 37 15- 10-1 5- O D. 154 10- 5 10 15

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Understanding and Identifying the Minimum Cost in a Linear Programming Problem** **Objective Function:** The goal is to graph the constant-cost lines for the objective function \( C = 3x + 4y \) through the points (6,6) and (9,9). Use a straightedge to locate the corner point where the minimum cost occurs. Verify your solution by constructing a corner point table. **Detailed Graph Explanation:** 1. **Graph Area:** - The main graph on the left displays a shaded polygon region, which represents feasible solutions to the problem. The constraints form the boundaries of the region. - Corner points listed are: (0,15), (15,15), (15,0), (6,6), (3,4), (0,11), (0,15), and (9,9). 2. **Objective Function Lines:** - These are constant-cost lines represented by dashed lines. - Each line marks combinations of \((x, y)\) that yield the same cost according to the function \( C = 3x + 4y \). 3. **Determining the Minimum Cost:** - A straightedge method is employed to trace lines parallel to the dashed constant-cost lines until they touch the last point on the feasible region, identifying the corner point for potential minimum cost. 4. **Corner Point Table Construction:** - You will evaluate the cost at each corner point by substituting the coordinates into the objective function \( C = 3x + 4y \). - The objective function values are calculated for each of the feasible region's corner points, identifying the point with the minimum cost. **Multiple Choice Question:** **Task:** Identify which graph (A, B, C, or D) illustrates the appropriate constant-cost lines for the provided feasible region. **Graphs Explanation:** - Four small graphs labeled A, B, C, and D show variations of the main graph, indicating different lines and their orientations. - You need to compare these with the main graph to determine which one correctly extends the constant-cost line methodology. To answer the question, align the constant-cost lines visually with the primary graph's format to choose the correct option. This exercise involves skills in graph reading, linear inequality understanding, and optimization techniques in linear programming.
Transcribed Image Text:**Understanding and Identifying the Minimum Cost in a Linear Programming Problem** **Objective Function:** The goal is to graph the constant-cost lines for the objective function \( C = 3x + 4y \) through the points (6,6) and (9,9). Use a straightedge to locate the corner point where the minimum cost occurs. Verify your solution by constructing a corner point table. **Detailed Graph Explanation:** 1. **Graph Area:** - The main graph on the left displays a shaded polygon region, which represents feasible solutions to the problem. The constraints form the boundaries of the region. - Corner points listed are: (0,15), (15,15), (15,0), (6,6), (3,4), (0,11), (0,15), and (9,9). 2. **Objective Function Lines:** - These are constant-cost lines represented by dashed lines. - Each line marks combinations of \((x, y)\) that yield the same cost according to the function \( C = 3x + 4y \). 3. **Determining the Minimum Cost:** - A straightedge method is employed to trace lines parallel to the dashed constant-cost lines until they touch the last point on the feasible region, identifying the corner point for potential minimum cost. 4. **Corner Point Table Construction:** - You will evaluate the cost at each corner point by substituting the coordinates into the objective function \( C = 3x + 4y \). - The objective function values are calculated for each of the feasible region's corner points, identifying the point with the minimum cost. **Multiple Choice Question:** **Task:** Identify which graph (A, B, C, or D) illustrates the appropriate constant-cost lines for the provided feasible region. **Graphs Explanation:** - Four small graphs labeled A, B, C, and D show variations of the main graph, indicating different lines and their orientations. - You need to compare these with the main graph to determine which one correctly extends the constant-cost line methodology. To answer the question, align the constant-cost lines visually with the primary graph's format to choose the correct option. This exercise involves skills in graph reading, linear inequality understanding, and optimization techniques in linear programming.
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