Xq. Xg 20 k variables, determine the initial system for the linear programming problem. Use s, for the first constraint and s, for the second constraint. First constraint Second constraint Objective function 2 0 simplex tableau by filling in the blanks below.
Xq. Xg 20 k variables, determine the initial system for the linear programming problem. Use s, for the first constraint and s, for the second constraint. First constraint Second constraint Objective function 2 0 simplex tableau by filling in the blanks below.
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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Question
7.
![(A) Using slack variables, determine the initial system for the linear programming problem. Use \( s_1 \) for the first constraint and \( s_2 \) for the second constraint.
First constraint
Second constraint
Objective function
\[
x_1, x_2, s_1, s_2 \geq 0
\]
- Maximize \( P = 45x_1 + x_2 \)
- Subject to:
- \( 4x_1 + x_2 \leq 20 \)
- \( x_1 + 5x_2 \leq 20 \)
- \( x_1, x_2 \geq 0 \)
(B) Write the simplex tableau by filling in the blanks below.
| | \( x_1 \) | \( x_2 \) | \( s_1 \) | \( s_2 \) | P |
|-------|-----------|-----------|-----------|-----------|----|
| \( s_1 \) | | | 1 | 0 | 20 |
| \( s_2 \) | | | 0 | 1 | 20 |
| PL | | | | | |
The pivot element is located in the (dropdown) column and (dropdown) row.
The entering variable is (dropdown) and the exiting variable is (dropdown).
(C) Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- A. The maximum value is \( P = \) when \( x_1 = \) and \( x_2 = \). (Type integers or simplified fractions.)
- B. There is no optimal solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5af4684-8c2d-4df0-9359-946952989e9a%2F9617745d-0112-4aaf-a087-f74c61c21d28%2F01ruq2i_processed.png&w=3840&q=75)
Transcribed Image Text:(A) Using slack variables, determine the initial system for the linear programming problem. Use \( s_1 \) for the first constraint and \( s_2 \) for the second constraint.
First constraint
Second constraint
Objective function
\[
x_1, x_2, s_1, s_2 \geq 0
\]
- Maximize \( P = 45x_1 + x_2 \)
- Subject to:
- \( 4x_1 + x_2 \leq 20 \)
- \( x_1 + 5x_2 \leq 20 \)
- \( x_1, x_2 \geq 0 \)
(B) Write the simplex tableau by filling in the blanks below.
| | \( x_1 \) | \( x_2 \) | \( s_1 \) | \( s_2 \) | P |
|-------|-----------|-----------|-----------|-----------|----|
| \( s_1 \) | | | 1 | 0 | 20 |
| \( s_2 \) | | | 0 | 1 | 20 |
| PL | | | | | |
The pivot element is located in the (dropdown) column and (dropdown) row.
The entering variable is (dropdown) and the exiting variable is (dropdown).
(C) Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- A. The maximum value is \( P = \) when \( x_1 = \) and \( x_2 = \). (Type integers or simplified fractions.)
- B. There is no optimal solution.
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