Problem 7.1-3 Change the objective function to W = 3y1 + 5y2. I would apprecite
ID: 3145947 • Letter: P
Question
Problem 7.1-3
Change the objective function to W = 3y1 + 5y2.
I would apprecite if you can show all steps. thank you
(e) Change the coefficient of x2 in constraint 2 to a22 = 2. (f) Change the coefficient of x in constraint 1 to a1 8 = 3. his set of equations. DI 7.1-3. Consider the following problem. Minmize 5y +4y2 the dual problem from the by solving the dual olution subject to is changed to 4x3, y1 +2y2 and Because this primal problem has more functional constraints than variables, suppose that the simplex method has been applied di- rectly to its dual problem. If we let xs and x denote the slack vari- ables for this dual problem, the resulting final simplex tableau is hether the previous optimal ented in Sec. 5.3 to identify inal set of equations after it Basic in the original problem given Variable Eq. Zx x2 x3 xxsSide Coefficient of Right ge in the original problem is introduced into the model as (0) 1 3 0 2 0 19 x21 0 11 -11 (2) 2 031 23 X4 4x3 +2xnew For each of the following independent chngges in the original pri- mal model, you now are to conduct sensitivity analysis by directly investigating the effect on the dual problem and then inferring the complementary effect on the primal problem. For each change, ap- ply the procedure for sensitivity analysis summarized at the end of Sec. 7.1 to the dual problem (do not reoptimize), and then give your conclusions as to whether the current basic solution for the primal problem still is feasible and whether it still is optimal. Then check your conclusions by a direct graphical analysis of the pri- mal problem. .5 0 0, xnew . whether the previous optimal sstill optimal.Explanation / Answer
Optimal Solution: p = 6; y1 = 2, y2 = 0
Tableau #1
y1 y2 s1 s2 s3 s4 s5 s6 -p
4 3 -1 0 0 0 0 0 0 4
2 1 0 -1 0 0 0 0 0 3
1 2 0 0 -1 0 0 0 0 1
1 1 0 0 0 -1 0 0 0 2
1 0 0 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 -1 0 0
3 5 0 0 0 0 0 0 1 0
Tableau #2
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 3 -1 0 0 0 4 0 0 4
0 1 0 -1 0 0 2 0 0 3
0 2 0 0 -1 0 1 0 0 1
0 1 0 0 0 -1 1 0 0 2
1 0 0 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 -1 0 0
0 5 0 0 0 0 3 0 1 0
Tableau #3
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 -5 -1 0 4 0 0 0 0 0
0 -3 0 -1 2 0 0 0 0 1
0 2 0 0 -1 0 1 0 0 1
0 -1 0 0 1 -1 0 0 0 1
1 2 0 0 -1 0 0 0 0 1
0 1 0 0 0 0 0 -1 0 0
0 -1 0 0 3 0 0 0 1 -3
Tableau #4
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 5 1 0 -4 0 0 0 0 0
0 -3 0 -1 2 0 0 0 0 1
0 2 0 0 -1 0 1 0 0 1
0 -1 0 0 1 -1 0 0 0 1
1 2 0 0 -1 0 0 0 0 1
0 1 0 0 0 0 0 -1 0 0
0 -1 0 0 3 0 0 0 1 -3
Tableau #5
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 -1 1 -2 0 0 0 0 0 2
0 -1.5 0 -0.5 1 0 0 0 0 0.5
0 0.5 0 -0.5 0 0 1 0 0 1.5
0 0.5 0 0.5 0 -1 0 0 0 0.5
1 0.5 0 -0.5 0 0 0 0 0 1.5
0 1 0 0 0 0 0 -1 0 0
0 3.5 0 1.5 0 0 0 0 1 -4.5
Tableau #6
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 0 1 -2 0 0 0 -1 0 2
0 0 0 -0.5 1 0 0 -1.5 0 0.5
0 0 0 -0.5 0 0 1 0.5 0 1.5
0 0 0 0.5 0 -1 0 0.5 0 0.5
1 0 0 -0.5 0 0 0 0.5 0 1.5
0 1 0 0 0 0 0 -1 0 0
0 0 0 1.5 0 0 0 3.5 1 -4.5
Tableau #7
y1 y2 s1 s2 s3 s4 s5 s6 -p
0 0 1 0 0 -4 0 1 0 4
0 0 0 0 1 -1 0 -1 0 1
0 0 0 0 0 -1 1 1 0 2
0 0 0 1 0 -2 0 1 0 1
1 0 0 0 0 -1 0 1 0 2
0 1 0 0 0 0 0 -1 0 0
0 0 0 0 0 3 0 2 1 -6