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Solve the given linear programming problem using the table method. 1) Maximize P= 7x1 + 6x2 1) subject to 3x1 + x2 s 21 X1 + x2 s 10 x1 + 2x2 s 12 x1, x2 2 0 A) Max P = 66 at x1 = 6, x2 = 4 В) Маx Р - 68 аt xj 8, х2 2 С) Маx Р «65.5 at x 5.5, х2 - 45 D) Max P- 60 at xj 6, х2 3

Solve the given linear programming problem using the table method. 1) Maximize P= 7x1 + 6x2 1) subject to 3x1 + x2 s 21 X1 + x2 s 10 x1 + 2x2 s 12 x1, x2 2 0 A) Max P = 66 at x1 = 6, x2 = 4 В) Маx Р - 68 аt xj 8, х2 2 С) Маx Р «65.5 at x 5.5, х2 - 45 D) Max P- 60 at xj 6, х2 3

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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Certainly! Below is the transcription of the image as it would appear on an educational website, along with detailed explanations of the tables: --- ### Linear Programming Problem #### 1) Solve the given linear programming problem using the table method. **Objective:** Maximize \( P = 7x_1 + 6x_2 \) **Subject to:** - \( 3x_1 + x_2 \leq 21 \) - \( x_1 + x_2 \leq 10 \) - \( x_1 + 2x_2 \leq 12 \) - \( x_1, x_2 \geq 0 \) **Options for Maximum \( P \):** - **A)** \( \text{Max } P = 66 \text{ at } x_1 = 6, x_2 = 5 \) - **B)** \( \text{Max } P = 68 \text{ at } x_1 = 8, x_2 = 2 \) - **C)** \( \text{Max } P = 65.5 \text{ at } x_1 = 5.5, x_2 = 4.5 \) - **D)** \( \text{Max } P = 60 \text{ at } x_1 = 6, x_2 = 3 \) --- #### 2) Convert the given i-system to an e-system using slack variables. Construct a table of all basic solutions of the e-system. Indicate whether each basic solution is feasible. **Linear Inequality:** \( 9x_1 + 7x_2 \leq 63 \) **Conditions:** \( x_1, x_2 \geq 0 \) **Tables for Basic Solutions:** - **A)** - **Equation:** \( 9x_1 + 7x_2 + s_1 = 63 \) \[ \begin{array}{c|ccc} & x_1 & x_2 & s_1 \\ \hline (A) & 0 & 0 & 63 \\ (B) & 0 & 7 & 0 \\ (C) & 9 & 0 & 0 \\ \end{array} \] -
Transcribed Image Text:Certainly! Below is the transcription of the image as it would appear on an educational website, along with detailed explanations of the tables: --- ### Linear Programming Problem #### 1) Solve the given linear programming problem using the table method. **Objective:** Maximize \( P = 7x_1 + 6x_2 \) **Subject to:** - \( 3x_1 + x_2 \leq 21 \) - \( x_1 + x_2 \leq 10 \) - \( x_1 + 2x_2 \leq 12 \) - \( x_1, x_2 \geq 0 \) **Options for Maximum \( P \):** - **A)** \( \text{Max } P = 66 \text{ at } x_1 = 6, x_2 = 5 \) - **B)** \( \text{Max } P = 68 \text{ at } x_1 = 8, x_2 = 2 \) - **C)** \( \text{Max } P = 65.5 \text{ at } x_1 = 5.5, x_2 = 4.5 \) - **D)** \( \text{Max } P = 60 \text{ at } x_1 = 6, x_2 = 3 \) --- #### 2) Convert the given i-system to an e-system using slack variables. Construct a table of all basic solutions of the e-system. Indicate whether each basic solution is feasible. **Linear Inequality:** \( 9x_1 + 7x_2 \leq 63 \) **Conditions:** \( x_1, x_2 \geq 0 \) **Tables for Basic Solutions:** - **A)** - **Equation:** \( 9x_1 + 7x_2 + s_1 = 63 \) \[ \begin{array}{c|ccc} & x_1 & x_2 & s_1 \\ \hline (A) & 0 & 0 & 63 \\ (B) & 0 & 7 & 0 \\ (C) & 9 & 0 & 0 \\ \end{array} \] -
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