9.5
(a) We use u as a dual variable for the first constraint and v as a dual variable for the second constraint
of the primal LP. The dual is
min
s.t.
7u + 3v
u+v ≥5
u−v ≥1
u ≥ 0, v ≥ 0
(b) The graph of the primal and dual feasible regions are follows:
Dual
v
5
Primal
y
7
6
4
5
3
4
2
3
1
2
0
u
1
2
3
4
5
6
-1
1
x
0
1
2
3
4
5
-1
-2
-3
Using the graphical method, we find that the optimal solution to the primal is (x, y) = (5, 2) and the
primal optimal value is 27. Similarly, we find that the optimal solution to the dual is (u, v) = (3, 2),
and the dual optimal value is 27. Note that the optimal values of the primal and dual are equal, as
the Strong Duality Theorem would imply.
1