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
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:** \( 9x_1 + 7x_2 + s_1 = 63 \)
\[
\begin{array}{c|ccc}
& x_1 & x_2 & s_1 \\
\hline
(A) & 0 & 0 & 63 \\
(B) & 0 & 7 & 0 \\
(C) & 9 & 0 & 0 \\
\end{array}
\]
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ad954f6-3e43-4185-98a8-84783e08c6bc%2F04f79654-58d0-4ec0-b380-a2a466403db4%2F157z2l9_processed.png&w=3840&q=75)
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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