Lecture 5

To solve any equations…

Actions:

1. Multiply a row by a scalar.
2. Add / Subtract one row from another row.
3. Interchange two rows.

Canonical system

Use the row operations to simplify your main variables x1, x2, i.e. their coefficients must become 1. Once that’s done set the remaining variables equal to 0, and the resulting solution will allow a simplified answer to x1, and x2.

x3, x4, x5 – make all of these equal to 0 – i.e. zero!

Easy.

Summary

A basic feasible solution (bfs) is a basic solution in which the value of the basic variables is non-negative, i.e. either positive or equal to zero. Remember this!

How do you multiply a matrix?

Remember the point of intersection of the constraints is the solution for maximisation…, with the RHS right hand side being non-negative.

…by a single variable…

This is called scalar multiplication, you just multiply each variable in the matrix with the number.

…by another matrix

Matrix need to be compatible, i.e Row by column must match ie. 1 x 3 with a 3 x 1

multiply out , then add all the numbers together…

First row , First column

first row second column, with second column first row

first row, third column with third row first column