Optimization

108 Optimization: Algorithms and Applications

To maintain nonnegativity of the basic variables x

3

, x

4

, and x

5

, the variable

x

2

can take a maximum value of 10 in the equation

x

3

= 10 − x

2

and x

2

can take a maximum value of 4 in the equation

x

4

= 8 − 2x

2

Though we would like to take x

2

as large as possible to minimize the objec-

tive function, it can take a maximum value of 4 without making x

4

negative.

Thus, x

4

is the leaving basic variable. Note that if the coefcients of x

2

on

the left-hand side of the constraint equations were negative, then x

2

can be

increased to any larger value without violating the nonnegativity constraint

of the basi ...