Engineering Optimization: Theory and Practice, Fourth Edition

612 Integer Programming

x 1

Figure 10.4 Graphical solution of problem (E 3 ).

Step 3: The next branching process, with integer bounds onx 2 , leads to the following

problems:

Maximizef= 3 x 1 + 4 x 2

subject to (E 5 )

7 x 1 + 11 x 2 ≤ 88 , 3 x 1 −x 2 ≤ 21 , x 1 ≤ 5 , x 2 ≤ 4

and

Maximizef= 3 x 1 + 4 x 2

subject to (E 6 )

7 x 1 + 11 x 2 ≤ 88 , 3 x 1 −x 2 ≤ 21 , x 1 ≤ 5 , x 2 ≥ 5