Optimization

118 Optimization: Algorithms and Applications

Writing the modied objective function in terms of the nonbasic variables

using the rst and second constraint equations:

y

1

+ y

2

= 13 − 5x

1

+ 2x

2

+ x

3

This can also be done using the formula

ˆ

c c y N

N

T

N

T T

= − (4.33)

where

y c B

T

B

T

=

−1

(4.34)

By executing the MATLAB code (initial_cost.m), the cost coefcients for the

nonbasic variables can be obtained as

(-5, 2, 1)

With a minor modication of the MATLAB code (simplex.m), phase I code is

written in phase1.m. On executing the code, the following output is displayed

on the command window.

─────────────────────────────────────────

basic_set = 5 6 4

nonbasic_set = 1 2 3

Initial_Table =

1 0 0 3 2 0 10

0 1 0 2 -4 -1 3

0 0 1 3 4 0 16 ...