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y a b a 1 5 10 1 100 b 8 -4 -1 1 16 -2 3 1 45 7 -4 -2 1 a) What column is the pivot column? b) What row is the pivot row? c) What is the pivot number? C.

y a b a 1 5 10 1 100 b 8 -4 -1 1 16 -2 3 1 45 7 -4 -2 1 a) What column is the pivot column? b) What row is the pivot row? c) What is the pivot number? C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Table Data:** The table consists of a matrix used in the Simplex Method for linear programming. The matrix is organized into rows and columns and includes the following variables and constants: - Variables: \(x\), \(y\), \(z\), \(a\), \(b\), \(c\), \(p\) - Rows labeled: \(a\), \(b\), \(c\), \(p\) **Matrix Representation:** ``` | x y z a b c p ----|--------------------- a | 1 5 10 1 0 0 0 | 100 b | 8 -4 -1 0 1 0 0 | 16 c | -2 3 3 0 0 1 0 | 45 p | 7 -4 -2 0 0 0 1 | 0 ``` **Questions:** a) What column is the pivot column? - To find the pivot column, look for the most negative entry in the bottom row (row \(p\)) among the decision variables (\(x, y, z\)). b) What row is the pivot row? - For the pivot row, calculate the ratio of the right-hand side (the constants) to the corresponding positive pivot column entries. c) What is the pivot number? - The pivot number is the entry in the matrix located at the intersection of the pivot row and pivot column. In this context, it is assumed that the matrix data follows linear programming conventions, where the bottom row serves as the objective function coefficients, and the last column represents the constants in the constraints.
Transcribed Image Text:**Table Data:** The table consists of a matrix used in the Simplex Method for linear programming. The matrix is organized into rows and columns and includes the following variables and constants: - Variables: \(x\), \(y\), \(z\), \(a\), \(b\), \(c\), \(p\) - Rows labeled: \(a\), \(b\), \(c\), \(p\) **Matrix Representation:** ``` | x y z a b c p ----|--------------------- a | 1 5 10 1 0 0 0 | 100 b | 8 -4 -1 0 1 0 0 | 16 c | -2 3 3 0 0 1 0 | 45 p | 7 -4 -2 0 0 0 1 | 0 ``` **Questions:** a) What column is the pivot column? - To find the pivot column, look for the most negative entry in the bottom row (row \(p\)) among the decision variables (\(x, y, z\)). b) What row is the pivot row? - For the pivot row, calculate the ratio of the right-hand side (the constants) to the corresponding positive pivot column entries. c) What is the pivot number? - The pivot number is the entry in the matrix located at the intersection of the pivot row and pivot column. In this context, it is assumed that the matrix data follows linear programming conventions, where the bottom row serves as the objective function coefficients, and the last column represents the constants in the constraints.
Expert Solution
Step 1

pivot column is the column which has maximum value of p .

a) So, pivot column = x

i.e. x ,1, 8, -2 ,7 

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