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A. A company manufactures three goods, X; Y and Z, each of which is made from three types of input, A; B-and-C. Each unit of X requires 1 unit of A, 7 units of B.and 3 units of C. Each unit of Y requires 4 units of A, 3 units of B and 1 unit of C. Furthermore, one unit of Z-requires 2 units of A, 4 units of B-and-2-units of C. In a particular day's production the company uses up 105 units of A, 135 units of B and 55 units of C. T i. → Create an augmented matrix to represent the usage of A; B and C in the - day's production of x; y-and-z-units of X; Y-and-Z-respectively. 1

A. A company manufactures three goods, X; Y and Z, each of which is made from three types of input, A; B-and-C. Each unit of X requires 1 unit of A, 7 units of B.and 3 units of C. Each unit of Y requires 4 units of A, 3 units of B and 1 unit of C. Furthermore, one unit of Z-requires 2 units of A, 4 units of B-and-2-units of C. In a particular day's production the company uses up 105 units of A, 135 units of B and 55 units of C. T i. → Create an augmented matrix to represent the usage of A; B and C in the - day's production of x; y-and-z-units of X; Y-and-Z-respectively. 1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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A. A company manufactures three goods, X; Y and Z, each of which is made from three types of input, A; B and C. Each unit of X requires 1 unit of A, 7-units-of- B and 3 units of C. Each unit of Y requires 4 units of A, 3 units-of-B-and-1 unit. of C. Furthermore, one unit of Z-requires 2 units of A, 4 units of B and 2 units. of C. In a particular day's production the company uses up 105 units of A, 135. units of B and 55 units of C. ¶ i. → Create an augmented matrix to represent the usage of A; B-and-C-in-the- day's production of x; y-and-z-units of X; Y and Z.respectively. 1 ii. → Using Row reduction method, determine the values of x; -y-and-z. → 1 ¶ B.-Express the following system of equations in matrix form and solve it using. (elementary row operations) row reduction matrix method. -3x + y + z = 11 -x+y=z= -11 -5r+v+z = 3¶
Transcribed Image Text:A. A company manufactures three goods, X; Y and Z, each of which is made from three types of input, A; B and C. Each unit of X requires 1 unit of A, 7-units-of- B and 3 units of C. Each unit of Y requires 4 units of A, 3 units-of-B-and-1 unit. of C. Furthermore, one unit of Z-requires 2 units of A, 4 units of B and 2 units. of C. In a particular day's production the company uses up 105 units of A, 135. units of B and 55 units of C. ¶ i. → Create an augmented matrix to represent the usage of A; B-and-C-in-the- day's production of x; y-and-z-units of X; Y and Z.respectively. 1 ii. → Using Row reduction method, determine the values of x; -y-and-z. → 1 ¶ B.-Express the following system of equations in matrix form and solve it using. (elementary row operations) row reduction matrix method. -3x + y + z = 11 -x+y=z= -11 -5r+v+z = 3¶
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