Using the information in the table, determine the least expensive way to visit all of these cities, starting and ending in Buenos Aires.
a. Buenos Aires $\rightarrow$ Salta $\rightarrow$ Bahia Blanca $\rightarrow$ Tucuman $\rightarrow$ Buenos Aires
b. Buenos Aires $\rightarrow$ Tucuman $\rightarrow$ Salta $\rightarrow$ Bahia Blanca $\rightarrow$ Buenos Aires
c. Buenos Aires $\rightarrow$ Tucuman $\rightarrow$ Bahia Blanca $\rightarrow$ Salta $\rightarrow$ Buenos Aires
d. Buenos Aires $\rightarrow$ Bahia Blanca $\rightarrow$ Tucuman $\rightarrow$ Salta $\rightarrow$ Buenos Aires
Answer (2)
The least expensive way to visit all cities starting and ending in Buenos Aires is Route D, with a total cost of 825. Other routes cost more, with Route A being the most expensive at 1014. Thus, Route D is the optimal choice for minimizing travel expenses.
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Calculate the cost of Route a: Buenos Aires → Salta → Bahia Blanca → Tucuman → Buenos Aires, which is 1014 .
Calculate the cost of Route b: Buenos Aires → Tucuman → Salta → Bahia Blanca → Buenos Aires, which is 950 .
Calculate the cost of Route c: Buenos Aires → Tucuman → Bahia Blanca → Salta → Buenos Aires, which is 871 .
Calculate the cost of Route d: Buenos Aires → Bahia Blanca → Tucuman → Salta → Buenos Aires, which is 825 . Therefore, the least expensive route is d .
Explanation
Problem Analysis We are given a table of costs for travel between four cities: Buenos Aires, Salta, Tucuman, and Bahia Blanca. The problem asks us to find the least expensive route that starts and ends in Buenos Aires, visiting all four cities. We are given four possible routes.
Solution Strategy To find the least expensive route, we need to calculate the total cost for each of the given routes and compare them.
Calculating Cost of Route A Route a: Buenos Aires → Salta → Bahia Blanca → Tucuman → Buenos Aires. The cost is 238 + 275 + 229 + 272 = 1014 .
Calculating Cost of Route B Route b: Buenos Aires → Tucuman → Salta → Bahia Blanca → Buenos Aires. The cost is 272 + 203 + 275 + 200 = 950 .
Calculating Cost of Route C Route c: Buenos Aires → Tucuman → Bahia Blanca → Salta → Buenos Aires. The cost is 272 + 195 + 211 + 193 = 871 .
Calculating Cost of Route D Route d: Buenos Aires → Bahia Blanca → Tucuman → Salta → Buenos Aires. The cost is 200 + 229 + 203 + 193 = 825 .
Comparing Costs Comparing the total costs for each route, we have: Route a: 1014 Route b: 950 Route c: 871 Route d: 825 The least expensive route is Route d with a total cost of 825.
Final Answer Therefore, the least expensive way to visit all of these cities, starting and ending in Buenos Aires, is Buenos Aires → Bahia Blanca → Tucuman → Salta → Buenos Aires.
Examples
Imagine you are a travel agent planning a trip for a client who wants to visit several cities in a specific order, starting and ending at the same city. To minimize the travel expenses, you would use a similar approach to calculate the cost of different possible routes and identify the least expensive one. This problem demonstrates how to optimize travel routes based on cost, which is a common task in logistics and travel planning. For example, if the costs between cities are: Buenos Aires to Salta ($238), Bahia Blanca to Buenos Aires ($200), Tucuman to Salta ($203), and Bahia Blanca to Tucuman ($229), then finding the cheapest route involves summing the costs of each leg of the journey for all possible routes and comparing the totals.
