Engineering Optimization: Theory and Practice, Fourth Edition

162 Linear Programming I: Simplex Method

3.6 What elementary operations can be used to transform

2 x 1 +x 2 +x 3 = 9

x 1 +x 2 +x 3 = 6

2 x 1 + 3 x 2 +x 3 = 13

into

x 1 = 3

x 2 = 2

x 1 + 3 x 2 +x 3 = 10

Find the solution of this system by reducing into canonical form.

3.7 Find the solution of the following LP problem graphically:

Maximizef= 2 x 1 + 6 x 2

subject to

−x 1 +x 2 ≤ 1

2 x 1 +x 2 ≤ 2

x 1 ≥ 0 , x 2 ≥ 0

3.8 Find the solution of the following LP problem graphically:

Minimizef= − 3 x 1 + 2 x 2

subject to

0 ≤x 1 ≤ 4

1 ≤x 2 ≤ 6

x 1 +x 2 ≤ 5

3.9 Find the solution of the following LP problem graphically:

Minimizef= 3 x 1 + 2 x 2

subject to

8 x 1 +x 2 ≥ 8

2 x 1 +x 2 ≥ 6

x 1 + 3 x 2 ≥ 6

x 1 + 6 x 2 ≥ 8

x 1 ≥ 0 , x 2 ≥ 0