Business Mathematics MTH367 Lecture 3 Chapter 3 Systems

Business Mathematics MTH-367 Lecture 3

Chapter 3 Systems of Linear Equations (Continued)

Review • • • Two variable systems of equations Solution sets Graphical analysis The elimination procedure Systems of more than two equations with two variables only • Gaussian elimination method (2 x 2 system)

Today’s Topics • n-variable systems, n >2 • Application to product mix problem.

Main Points • The general idea is to transform the original system into diagonal form. • We can use short notations as well to solve the system e. g. can be written as:

• The vertical line is used to separate the left and right sides of an equation. • Each column to the left of the vertical line contains all the coefficients for one of the variables in the system

Gaussian elimination procedure for 3 x 3 system • The procedure of Gaussian elimination method for the 3 x 3 system is same as for 2 x 2 system. • First we will form coefficient transformation for 3 x 3 system, then convert it to transformed system.

Examples

Examples (contd. )

Examples (contd)

Examples (contd. )

Examples (contd. )

Examples (contd. )

Examples (contd. )

Examples (contd. )

Examples (contd. )

Applications Product mix problem: A variety of applications are concerned with determining the quantaties of different products which satisfy specific requirements.

Example • A company produces three products • Each needs to be processed through 3 different departments, with following data. Determine whethere any combination of three products which would exhaust the weekly capacities of the three departments?

Example (contd. ) Solution:

Summary • Gaussian elimination method for 3 x 3 system • Application to product mix problem

Next Lecture • • Functions Domain and Range of a function Multivariate functions Types of functions