E R?, z is the optimal value for each linear relaxation, and (x1, x2) is a corresponding solution. F Z= a, え= 16, x,-3.9 X <3 2 = az X;=6.2, 2,=3 2,= 5, x2=4 と;56 , >7

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After several iterations of the branch and bound algorithm applied to an integer program of the form

 

max c' x subject to Ax < b,
xƐN?
(3)
we obtain the diagram in Figure 2. Regarding the notations, N := {0,1, 2, ...}, A E R²×2, b e R²,
ce R?, z is the optimal value for each linear relaxation, and (x1, x2) is a corresponding solution. For
Z= a,
2, = 46, x,=3.9
= 3.9
ニ
2く3
Z = ag
X,=6.2, 2,=3
2, = 5, x2=4
と,<6
X, > 7
z = as
X=6, %2 = 1
2, = 7, X, =2.6
ノ
Figure 2: Branch and bound
each question below, give values of a1, a2, a3, a4; a5 E R so that the diagram will satisfy the stated
condition. If there are multiple values possible, then only one is sufficient.
1. (x1, x2) = (5, 4) is a solution to the integer program.
2. (x1, x2) = (6, 1) is a solution to the integer program.
3. (x1, x2) = (5,4) could be a solution but (x1, x2) = (6, 1) is not. In that case, what is the next step
of the branch and bound algorithm?
Transcribed Image Text:max c' x subject to Ax < b, xƐN? (3) we obtain the diagram in Figure 2. Regarding the notations, N := {0,1, 2, ...}, A E R²×2, b e R², ce R?, z is the optimal value for each linear relaxation, and (x1, x2) is a corresponding solution. For Z= a, 2, = 46, x,=3.9 = 3.9 ニ 2く3 Z = ag X,=6.2, 2,=3 2, = 5, x2=4 と,<6 X, > 7 z = as X=6, %2 = 1 2, = 7, X, =2.6 ノ Figure 2: Branch and bound each question below, give values of a1, a2, a3, a4; a5 E R so that the diagram will satisfy the stated condition. If there are multiple values possible, then only one is sufficient. 1. (x1, x2) = (5, 4) is a solution to the integer program. 2. (x1, x2) = (6, 1) is a solution to the integer program. 3. (x1, x2) = (5,4) could be a solution but (x1, x2) = (6, 1) is not. In that case, what is the next step of the branch and bound algorithm?
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