20- What is the best cost from X via Z to W?

Question

20- What is the best cost from X via Z to W?

BlackTom AI · Accepted Answer

Compute X→Z + Z→W: the cost of a route that goes from X to Z and then from Z to W is the sum of those two edge weights. Key concepts: in a weighted graph the cost of a path equals the sum of the weights of each traversed edge; "via Z" forces the path to include node Z between X and W.

Step-by-step reasoning:
1. Identify the relevant edges on the diagram. The edge connecting X and Z is labeled 6. The edge connecting Z and W is labeled 1.
2. Add those edge weights to get the total cost of X → Z → W:
   - Cost(X → Z) = 6
   - Cost(Z → W) = 1
   - Total cost = 6 + 1
3. Perform the arithmetic:
   - 6 + 1 = 7

Why this is correct: the path specified explicitly goes through Z, so any direct edge X→W (weight 3) is not allowed. The path cost must include both the X–Z and Z–W edges; summing them yields 7.

Why the other options are incorrect:
- 3: equals the direct edge X→W but does not go via Z, so it doesn't satisfy "via Z."
- 8: no combination of X→Z and Z→W edges in the diagram sums to 8; it's not the sum of 6 and 1.
- 6: equals only the X→Z segment and omits the Z→W segment, so it understates the required total.

Conclusion: Adding the weights 6 (X→Z) and 1 (Z→W) gives the best cost via Z to W as 7, which matches the provided correct answer.

20- What is the best cost from X via Z to W?Single choice

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