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Solve the given linear programming problem using the table method. 3) Maximize P= 6x1 + 7x2

Solve the given linear programming problem using the table method. 3) Maximize P= 6x1 + 7x2

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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**Page 1 REVIEW** **Solve the given linear programming problem using the table method.** 3) Maximize \( P = 6x_1 + 7x_2 \) Subject to: - \( 2x_1 + 3x_2 \leq 12 \) - \( 2x_1 + x_2 \leq 8 \) - \( x_1, x_2 \geq 0 \) Options: - A) \( \text{Max } P = 32 \text{ at } x_1 = 3, x_2 = 2 \) - B) \( \text{Max } P = 55 \text{ at } x_1 = 4, x_2 = 4 \) - C) \( \text{Max } P = 32 \text{ at } x_1 = 2, x_2 = 3 \) - D) \( \text{Max } P = 24 \text{ at } x_1 = 4, x_2 = 0 \) 3) _______ **Graph the system of inequalities.** 4) Inequalities: - \( x_1 + x_2 \leq 12 \) - \( 2x_1 + x_2 \leq 20 \) - \( x_1, x_2 \geq 0 \) **Graphs:** **A) Explanation:** - The graph shows a coordinate plane with \( x_1 \) on the horizontal axis and \( x_2 \) on the vertical axis. - The graph has a shaded area that represents the feasible region defined by the inequalities. - The lines for \( x_1 + x_2 = 12 \), \( 2x_1 + x_2 = 20 \), and the axes \( x_1 = 0 \), \( x_2 = 0 \) are clearly marked. - Key points, such as intersections on the feasible region, are labeled. **B) Description:** - Similar to graph A, this graph also represents the same inequalities in a coordinate plane. - The feasible region is slightly different, as shown by the altered intersection points and shaded area. - The constraints are depicted by straight lines
Transcribed Image Text:**Page 1 REVIEW** **Solve the given linear programming problem using the table method.** 3) Maximize \( P = 6x_1 + 7x_2 \) Subject to: - \( 2x_1 + 3x_2 \leq 12 \) - \( 2x_1 + x_2 \leq 8 \) - \( x_1, x_2 \geq 0 \) Options: - A) \( \text{Max } P = 32 \text{ at } x_1 = 3, x_2 = 2 \) - B) \( \text{Max } P = 55 \text{ at } x_1 = 4, x_2 = 4 \) - C) \( \text{Max } P = 32 \text{ at } x_1 = 2, x_2 = 3 \) - D) \( \text{Max } P = 24 \text{ at } x_1 = 4, x_2 = 0 \) 3) _______ **Graph the system of inequalities.** 4) Inequalities: - \( x_1 + x_2 \leq 12 \) - \( 2x_1 + x_2 \leq 20 \) - \( x_1, x_2 \geq 0 \) **Graphs:** **A) Explanation:** - The graph shows a coordinate plane with \( x_1 \) on the horizontal axis and \( x_2 \) on the vertical axis. - The graph has a shaded area that represents the feasible region defined by the inequalities. - The lines for \( x_1 + x_2 = 12 \), \( 2x_1 + x_2 = 20 \), and the axes \( x_1 = 0 \), \( x_2 = 0 \) are clearly marked. - Key points, such as intersections on the feasible region, are labeled. **B) Description:** - Similar to graph A, this graph also represents the same inequalities in a coordinate plane. - The feasible region is slightly different, as shown by the altered intersection points and shaded area. - The constraints are depicted by straight lines
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