3. (25 pts) The five residents of Hometown live in houses represented by the let

Question

3. (25 pts) The five residents of Hometown live in houses represented by the letters "A" through "E" as shown on the left side of Figure 1. The offices where they will be working are represented by their matching letters on the island of Worktawn. Because a river lies between Hometown and Worktw the residents are unable to get to work. They have in their budget enough funds to build two bridges that could connect Hometown and Worktawn The locations where these bridges could be built are indicated by the 1x3 hashed tiles. The two bridges can only be built in these approved areas. Once the bridges are built, the residents would then be able to commute to work. A commuter wil always take the shortest path from home to work and can only travel in up, down, left, or right directions (no diagonals). Each tile represents a 1-km-by-1-km distance. As an example, if bridge four were built, resident "E' would have to travel 10 km to reach his workplace Question: Which two bridges should be built in order to minimize the total commuting distance to all residents? You must give a thorough and quantitative basis for your answer. Hometown Worktown Bridge proposals connecting Hometown to Worktown

Explanation / Answer

Bridges ONE and THREE should be built, as minimum possible distances benefitting each one of them and collective good for everyone will be :

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