Question

a, d, b, c, a 136
a, d, c, b, a 136
which hamilton circuits are the optimal solutions?

• a, b, c, d, a and a, d, c, b, a

○ a, c, b, d, a and a, d, b, c, a
○ a, b, d, c, a and a, c, d, b, a
what is the weight of the optimal solution?

Explanation:

Step1: Analyze the Hamilton Circuits

From the table, we have two circuits: \( A, D, B, C, A \) (weight 136) and \( A, D, C, B, A \) (weight 134). The optimal solution (minimum weight) should be the one with the lower weight. Also, the symmetric circuit (reverse) of \( A, D, C, B, A \) is \( A, B, C, D, A \), and we check the options. The first option has \( A, B, C, D, A \) (reverse of \( A, D, C, B, A \)) and \( A, D, C, B, A \), which matches the lower weight (134 vs 136).

Step2: Determine the Weight

The weight of the optimal solution (the circuit with lower weight) is 134, as seen from the table for \( A, D, C, B, A \) (and its reverse \( A, B, C, D, A \)).

Answer:

For the first sub - question (optimal Hamilton circuits): A. A, B, C, D, A and A, D, C, B, A
For the second sub - question (weight of optimal solution): 134