use the complete weighted graph shown to answer the question.

jon is a traveling salesman for a pharmaceutical company. his territory includes 5 cities and he needs to find the least expensive route to the cities and home. starting at city a, which of the following is the optimal route using the nearest neighbor method?

i. a, e, c, b, d, a
ii. a, e, b, d, c, a
iii. a, e, d, b, c, a
iv. a, e, d, c, b, a

Question

use the complete weighted graph shown to answer the question.

jon is a traveling salesman for a pharmaceutical company. his territory includes 5 cities and he needs to find the least expensive route to the cities and home. starting at city a, which of the following is the optimal route using the nearest neighbor method?

i. a, e, c, b, d, a
ii. a, e, b, d, c, a
iii. a, e, d, b, c, a
iv. a, e, d, c, b, a

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Nearest Neighbor Method", "Weighted Graph", "Edge Weight Identification" ], "new_concepts": [], "current_concepts": [ "Nearest Neighbor Method", "Weighted Graph", "Edge Weight Identification", "Hamilton Circuit" ] } ## Identify edge weights from starting vertex A $$ \begin{aligned} &\text{From } A \text{, the available edges to unvisited vertices } \{B, C, D, E\} \text{ are:} \ &w(A, B) = 100 \ &w(A, C) = 250 \ &w(A, D) = 103 \ &w(A, E) = 95 \ &\min\{100, 250, 103, 95\} = 95 \implies \text{Choose vertex } E \end{aligned} $$ ## Identify next vertices from E, then D, then B $$ \begin{aligned} &\text{From } E \text{, available unvisited vertices are } \{B, C, D\}: \ &w(E, B) = 160, \quad w(E, C) = 180, \quad w(E, D) = 151 \ &\min\{160, 180, 151\} = 151 \implies \text{Choose vertex } D \ \ &\text{From } D \text{, available unvisited vertices are } \{B, C\}: \ &w(D, B) = 87, \quad w(D, C) = 170 \ &\min\{87, 170\} = 87 \implies \text{Choose vertex } B \ \ &\text{From } B \text{, the only remaining unvisited vertex is } C: \ &\text{Choose vertex } C \end{aligned} $$ ## Complete the Hamilton circuit back to A $$ \begin{aligned} &\text{From } C \text{, return to the starting vertex } A. \ &\text{The complete route is: } A \to E \to D \to B \to C \to A \end{aligned} $$

I. A, E, C, B, D, A

II. A, E, B, D, C, A

III. A, E, D, B, C, A

IV. A, E, D, C, B, A

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Nearest Neighbor Method" ] }

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QUESTION IMAGE

Question

Explanation:

Identify edge weights from starting vertex A

Identify next vertices from E, then D, then B

Complete the Hamilton circuit back to A

Answer: