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Find the particular solution corresponding to the tableau. x= ], y = ¯‚ z=₁ u=¯‚ v=, M= X y 1 0 0 1 0 0 Z -4 1 7 u 7 4 12 V 2 7 6 -003 16 15 க்ஷி

Find the particular solution corresponding to the tableau. x= ], y = ¯‚ z=₁ u=¯‚ v=, M= X y 1 0 0 1 0 0 Z -4 1 7 u 7 4 12 V 2 7 6 -003 16 15 க்ஷி

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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**Finding the Particular Solution from a Linear Programming Tableau** In this exercise, we aim to find the particular solution corresponding to the given tableau. ### Tableau Explanation The tableau provided is a matrix that includes both the coefficients of the variables in the linear programming problem and the constants on the right side of the equations. Here is the representation of the tableau: ``` | x | y | z | u | v | M | ---------------------------- 0 | 0 | 1 |-4 | 7 | 2 | 0 | 16 1 | 1 | 0 | 1 | 4 | 7 | 0 | 15 2 | 0 | 0 | 7 |12 | 6 | 1 | 54 ``` - The columns labeled `x`, `y`, `z`, `u`, `v`, and `M` represent the variables in the equations. - The numbers to the right of the vertical line are the constants (or right-hand side values) for each equation. ### Goal Given this tableau, you are required to find the values of variables `x`, `y`, `z`, `u`, `v`, and `M` that correspond to a particular solution. It involves interpreting the tableau to determine the values of the basic and non-basic variables in this linear programming context. ### Solution Input Fields The solution should be entered in the fields provided: - \( x = \_\_ \) - \( y = \_\_ \) - \( z = \_\_ \) - \( u = \_\_ \) - \( v = \_\_ \) - \( M = \_\_ \) By analyzing the tableau, you can determine which variables are basic (those corresponding to identity matrix columns) and which are non-basic (those not corresponding to identity matrix columns) to find the values of each variable.
Transcribed Image Text:**Finding the Particular Solution from a Linear Programming Tableau** In this exercise, we aim to find the particular solution corresponding to the given tableau. ### Tableau Explanation The tableau provided is a matrix that includes both the coefficients of the variables in the linear programming problem and the constants on the right side of the equations. Here is the representation of the tableau: ``` | x | y | z | u | v | M | ---------------------------- 0 | 0 | 1 |-4 | 7 | 2 | 0 | 16 1 | 1 | 0 | 1 | 4 | 7 | 0 | 15 2 | 0 | 0 | 7 |12 | 6 | 1 | 54 ``` - The columns labeled `x`, `y`, `z`, `u`, `v`, and `M` represent the variables in the equations. - The numbers to the right of the vertical line are the constants (or right-hand side values) for each equation. ### Goal Given this tableau, you are required to find the values of variables `x`, `y`, `z`, `u`, `v`, and `M` that correspond to a particular solution. It involves interpreting the tableau to determine the values of the basic and non-basic variables in this linear programming context. ### Solution Input Fields The solution should be entered in the fields provided: - \( x = \_\_ \) - \( y = \_\_ \) - \( z = \_\_ \) - \( u = \_\_ \) - \( v = \_\_ \) - \( M = \_\_ \) By analyzing the tableau, you can determine which variables are basic (those corresponding to identity matrix columns) and which are non-basic (those not corresponding to identity matrix columns) to find the values of each variable.
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