LINEAR MATHEMATICAL
MODELS
(Open Course)
(other than B Sc students)
Fifth semester
School of Distance Education
Calicut University
, Prepared by : Sreehari T
Asst professor in mathematics
SDE, Calicut university
Scrutinized by: Dr. Bijumon. R,
Associate Professor & Head,
Dept. of Mathematics,
Mahathma Gandhi College, Irittiy
DISCLAIMER
"The author(s) shall be solely responsible
,Contents
1 Linear Functions 1
1.1 Slopes and Equation of Lines . . . . . . . . . . . . 1
1.1.1 Slope of line . . . . . . . . . . . . . . . . 3
1.1.2 Equation of Line . . . . . . . . . . . . . . 5
1.1.3 Graph of a Line . . . . . . . . . . . . . . . 9
1.2 Linear Functions and Applications . . . . . . . . . 12
1.2.1 Linear function . . . . . . . . . . . . . . . 12
1.2.2 The Least Square Line . . . . . . . . . . . 17
1.2.3 Solutions of Linear Systems by the Eche-
lon Method . . . . . . . . . . . . . . . . . 24
1.2.4 Solution of Linear Systems by the Gauss-
Jordan Method . . . . . . . . . . . . . . . 29
1.2.5 Addition and Subtraction of Matrices . . . 35
1.2.6 Multiplication of Matrices . . . . . . . . . 38
1.2.7 Matrix Inverses . . . . . . . . . . . . . . . 40
1.2.8 Input-Output Models . . . . . . . . . . . . 47
2 Linear Programming: The Graphical Method 50
2.1 Graphing Linear Inequalities . . . . . . . . . . . . 50
, 2.1.1 Linear Inequality . . . . . . . . . . . . . . 50
2.1.2 Systems of Inequalities . . . . . . . . . . . 54
2.2 Solving Linear Programming Problems Graphically 58
2.3 Applications of Linear Programming . . . . . . . . 64
MODELS
(Open Course)
(other than B Sc students)
Fifth semester
School of Distance Education
Calicut University
, Prepared by : Sreehari T
Asst professor in mathematics
SDE, Calicut university
Scrutinized by: Dr. Bijumon. R,
Associate Professor & Head,
Dept. of Mathematics,
Mahathma Gandhi College, Irittiy
DISCLAIMER
"The author(s) shall be solely responsible
,Contents
1 Linear Functions 1
1.1 Slopes and Equation of Lines . . . . . . . . . . . . 1
1.1.1 Slope of line . . . . . . . . . . . . . . . . 3
1.1.2 Equation of Line . . . . . . . . . . . . . . 5
1.1.3 Graph of a Line . . . . . . . . . . . . . . . 9
1.2 Linear Functions and Applications . . . . . . . . . 12
1.2.1 Linear function . . . . . . . . . . . . . . . 12
1.2.2 The Least Square Line . . . . . . . . . . . 17
1.2.3 Solutions of Linear Systems by the Eche-
lon Method . . . . . . . . . . . . . . . . . 24
1.2.4 Solution of Linear Systems by the Gauss-
Jordan Method . . . . . . . . . . . . . . . 29
1.2.5 Addition and Subtraction of Matrices . . . 35
1.2.6 Multiplication of Matrices . . . . . . . . . 38
1.2.7 Matrix Inverses . . . . . . . . . . . . . . . 40
1.2.8 Input-Output Models . . . . . . . . . . . . 47
2 Linear Programming: The Graphical Method 50
2.1 Graphing Linear Inequalities . . . . . . . . . . . . 50
, 2.1.1 Linear Inequality . . . . . . . . . . . . . . 50
2.1.2 Systems of Inequalities . . . . . . . . . . . 54
2.2 Solving Linear Programming Problems Graphically 58
2.3 Applications of Linear Programming . . . . . . . . 64
