While staying in Jerusalem, Israel, you decide to visit three other cities: Tel Aviv, Holon, and Ra'anana. The following table shows the costs associated with traveling to and from each city, with all costs listed in Israeli new shekalim (NIS):
| Origin and Destination | Cost (NIS) |
| ---------------------- | ---------- |
| Jerusalem to Tel Aviv | 269 |
| Jerusalem to Holon | 201 |
| Jerusalem to Ra'anana | 281 |
| Tel Aviv to Jerusalem | 235 |
| Tel Aviv to Holon | 263 |
| Tel Aviv to Ra'anana | 203 |
| Holon to Jerusalem | 150 |
| Holon to Tel Aviv | 198 |
| Holon to Ra'anana | 290 |
| Ra'anana to Jerusalem | 176 |
| Ra'anana to Tel Aviv | 234 |
| Ra'anana to Holon | 218 |
Answer (2)
The cheapest route from Jerusalem visiting Tel Aviv, Holon, and Ra'anana, and returning to Jerusalem has been identified as Jerusalem → Holon → Tel Aviv → Ra'anana → Jerusalem with a total cost of 778 NIS. This route offers the lowest travel expenses among all possible routes considered.
;
List all possible routes starting from Jerusalem, visiting Tel Aviv, Holon, and Ra'anana, and returning to Jerusalem.
Calculate the total cost for each route by summing the costs of each leg of the journey.
Compare the total costs of all possible routes.
Identify the route with the minimum total cost: 778
Explanation
Problem Analysis We are given the costs of traveling between Jerusalem, Tel Aviv, Holon, and Ra'anana. Our goal is to find the cheapest route that starts in Jerusalem, visits Tel Aviv, Holon, and Ra'anana, and then returns to Jerusalem.
Solution Strategy To solve this, we need to consider all possible routes and calculate the total cost for each route. Then, we can compare the costs and find the minimum.
Listing Possible Routes The possible routes are:
Jerusalem -> Tel Aviv -> Holon -> Ra'anana -> Jerusalem
Jerusalem -> Tel Aviv -> Ra'anana -> Holon -> Jerusalem
Jerusalem -> Holon -> Tel Aviv -> Ra'anana -> Jerusalem
Jerusalem -> Holon -> Ra'anana -> Tel Aviv -> Jerusalem
Jerusalem -> Ra'anana -> Tel Aviv -> Holon -> Jerusalem
Jerusalem -> Ra'anana -> Holon -> Tel Aviv -> Jerusalem
Calculating Route Costs Now, let's calculate the cost for each route using the given table:
C 1 = 269 + 263 + 290 + 176 = 998
C 2 = 269 + 203 + 290 + 150 = 912
C 3 = 201 + 198 + 203 + 176 = 778
C 4 = 201 + 290 + 234 + 235 = 960
C 5 = 281 + 234 + 263 + 150 = 928
C 6 = 281 + 218 + 198 + 235 = 932
Finding the Minimum Cost Comparing the costs, we find that the minimum cost is 778 NIS, which corresponds to the route: Jerusalem -> Holon -> Tel Aviv -> Ra'anana -> Jerusalem.
Final Answer Therefore, the cheapest route is Jerusalem -> Holon -> Tel Aviv -> Ra'anana -> Jerusalem, with a total cost of 778 NIS.
Examples
Imagine you are planning a delivery route for a package, starting from a central depot and needing to visit several locations before returning to the depot. This problem is similar to finding the shortest delivery route to minimize fuel costs and time. By calculating the costs of all possible routes and comparing them, you can determine the most efficient path. This approach is also used in logistics and transportation to optimize routes for delivery trucks, buses, and other vehicles, saving time and money.
