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