Consider the following LP: Maximize z = 3x1 + 2x2 Subject to: 2x1 +52 8 3x17x210 #1, #20 The optimal tableau for this LP, where s; is the slack variable for constraint i, is as follows: B.V.1 T2 81 82 R.H.S. 21050 1 10 81 0 0 1/3 1 -2/3 4/3 1 0 1 7/3 0 1/3 10/3 If the right hand side of the second constraint changes to b2, what is the range of b₂ such that the current basic feasible solution remains optimal? Round all non-integer values to two decimal places, and use infty to represent oo. sh₂s
Consider the following LP: Maximize z = 3x1 + 2x2 Subject to: 2x1 +52 8 3x17x210 #1, #20 The optimal tableau for this LP, where s; is the slack variable for constraint i, is as follows: B.V.1 T2 81 82 R.H.S. 21050 1 10 81 0 0 1/3 1 -2/3 4/3 1 0 1 7/3 0 1/3 10/3 If the right hand side of the second constraint changes to b2, what is the range of b₂ such that the current basic feasible solution remains optimal? Round all non-integer values to two decimal places, and use infty to represent oo. sh₂s
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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![### Linear Programming Problem
Consider the following Linear Programming (LP) problem:
Maximize \( z = 3x_1 + 2x_2 \)
**Subject to:**
\[
\begin{align*}
2x_1 + 5x_2 & \leq 8 \\
3x_1 + 7x_2 & \leq 10 \\
x_1, x_2 & \geq 0
\end{align*}
\]
The optimal tableau for this LP, where \( s_i \) is the slack variable for constraint \( i \), is as follows:
\[
\begin{array}{c|ccc|cc|c}
\text{B.V.} & x_1 & x_2 & s_1 & s_2 & \text{R.H.S.} \\
\hline
s_1 & 1 & 0 & 5/3 & 1/3 & 10 \\
z & 0 & 1/3 & -2/3 & 4/3 & 10/3 \\
x_1 & 0 & 7/3 & 1/3 & 10/3 & 1/3
\end{array}
\]
**Explanation of the Tableau:**
- **B.V. (Basic Variable):** Indicates the basic variables in the current solution.
- **\( x_1, x_2, s_1, s_2 \):** Corresponds to the decision variables and slack variables.
- **R.H.S.:** Represents the right-hand side values of the constraints in the current solution.
**Problem Assessment:**
If the right hand side of the second constraint changes to \( b_2 \), what is the range of \( b_2 \) such that the current basic feasible solution remains optimal? Round all non-integer values to two decimal places and use \( \infty \) to represent ∞.
### Requirements
\[ \boxed{\leq b_2 \leq } \]
This section prepares students to understand changes in constraints and their effect on the feasibility and optimality of the solution in linear programming problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7f7e91-311f-40b2-8ef2-058480eb16a0%2Fbb84f787-7837-471b-8454-c187617db890%2Fqfg9ks5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Linear Programming Problem
Consider the following Linear Programming (LP) problem:
Maximize \( z = 3x_1 + 2x_2 \)
**Subject to:**
\[
\begin{align*}
2x_1 + 5x_2 & \leq 8 \\
3x_1 + 7x_2 & \leq 10 \\
x_1, x_2 & \geq 0
\end{align*}
\]
The optimal tableau for this LP, where \( s_i \) is the slack variable for constraint \( i \), is as follows:
\[
\begin{array}{c|ccc|cc|c}
\text{B.V.} & x_1 & x_2 & s_1 & s_2 & \text{R.H.S.} \\
\hline
s_1 & 1 & 0 & 5/3 & 1/3 & 10 \\
z & 0 & 1/3 & -2/3 & 4/3 & 10/3 \\
x_1 & 0 & 7/3 & 1/3 & 10/3 & 1/3
\end{array}
\]
**Explanation of the Tableau:**
- **B.V. (Basic Variable):** Indicates the basic variables in the current solution.
- **\( x_1, x_2, s_1, s_2 \):** Corresponds to the decision variables and slack variables.
- **R.H.S.:** Represents the right-hand side values of the constraints in the current solution.
**Problem Assessment:**
If the right hand side of the second constraint changes to \( b_2 \), what is the range of \( b_2 \) such that the current basic feasible solution remains optimal? Round all non-integer values to two decimal places and use \( \infty \) to represent ∞.
### Requirements
\[ \boxed{\leq b_2 \leq } \]
This section prepares students to understand changes in constraints and their effect on the feasibility and optimality of the solution in linear programming problems.
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