1. EMGT 501
HW #2
4.4-6(b) (c)
6.1-4,
6.1-5
Due Day: Sep. 21

2. 4.4-6 Consider the following problem.
(b) Work through the simplex method step by step in tabular form.
(c) Use a software package based on the simplex method to solve
the problem.

3. . 3 / 230 with ) 80 , 50 20 ( *) *, solution Optimal = Z x 4.4-6 (b)
Basis Z X 1 2 3 4 5 6
RHS -2 -4 -3 60 40 80 -1
3/4
1/2
1/4 15
5/4
3/2
-1/4 25
-5/4
-3/4 35
11/6
5/6
2/3
230/3
1/3
-1/3
20/3 X
5/6 1
-1/6
2/3
50/3 3 X
-5/3
-2/3
-1/3 1
80/3 6
(c) . 3 /
230
with ) 80 , 50 20 ( *) *,
solution
Optimal 6 5 4 2 1 = Z x

4. 6.1-4
For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain.
(a) Maximize
subject to
(b) Maximize
subject to
and
and

5. 6.1-4 (a) Dual formulation becomes
Min
s.t.
# of constraints of Dual = 3
# of constraints of Primal = 5
So, Dual is better than Primal because the size of B-1 in Dual is smaller than that of Primal.

6. (b) Dual formulation becomes
Min
s.t.
# of constraints of Dual = 5
# of constraints of Primal = 3
So, Primal is better than Dual because the size of B-1 in Primal is smaller than that of Dual.

7. 6.1-5
Consider the following problem.
Maximize
subject to
and
(a) Construct the dual problem.
(b) Use duality theory to show that the optimal solution
for the primal problem has

8. 6.1-5
(a)
Min
s.t.
(b)
It is clear that Z*=0, y1*=0, y2*=0.