Consider the following LP:
Maximize z=4x1+5x2+3x3
Subject to:
x1+x2+4x3≤6
x1+2x2+x3≤7
x1+4x2+2x3≤12
a) Add slack variables x4, x5 and x6, and perform iterations of the simplex algorithm. Show each completed iteration using tableau. The final (filled) tableau of the primal must be provided.
|
Basis
|
z
|
x1
|
x2
|
x3
|
x4
|
x5
|
x6
|
RHS
|
|
z
|
1
|
0
|
0
|
|
|
|
0
|
|
|
x1
|
0
|
1
|
0
|
|
|
|
0
|
|
|
x2
|
0
|
0
|
1
|
|
|
|
0
|
|
|
x6
|
0
|
0
|
0
|
|
|
|
1
|
|
b) Write the dual of this LP.