While abroad in Cairo, Egypt, you want to visit three other cities: Damanhur, Alexandria, and Suez. The following table details the costs of traveling to and from each city. All costs are given in Egyptian pounds (EGP).
| Origin and Destination | Cost (EGP) |
| :----------------------- | :--------- |
| Cairo to Damanhur | 153 |
| Cairo to Alexandria | 171 |
| Cairo to Suez | 130 |
| Damanhur to Cairo | 143 |
| Damanhur to Alexandria | 174 |
| Damanhur to Suez | 182 |
| Alexandria to Cairo | 167 |
| Alexandria to Damanhur | 192 |
| Alexandria to Suez | 144 |
| Suez to Cairo | 133 |
| Suez to Damanhur | 156 |
| Suez to Alexandria | 156 |
Answer (2)
The cheapest route to visit Damanhur, Alexandria, and Suez, starting and ending in Cairo, is Cairo -> Damanhur -> Alexandria -> Suez -> Cairo, with a total cost of 604 EGP. Other routes are more expensive. This approach systematically calculates costs for all possible routes to find the least expensive option.
;
List all possible routes starting and ending in Cairo.
Calculate the total cost for each route by summing the costs of each leg of the journey.
Compare the total costs of all routes.
Identify the route with the minimum total cost: Cairo -> Damanhur -> Alexandria -> Suez -> Cairo, costing 604 EGP.
Explanation
Understanding the Problem We want to find the cheapest route to visit Damanhur, Alexandria, and Suez, starting and ending in Cairo. We have the costs of traveling between each pair of cities.
Listing Possible Routes We need to list all possible routes, calculate the total cost for each route, and then find the route with the minimum cost. The possible routes are:
Cairo -> Damanhur -> Alexandria -> Suez -> Cairo
Cairo -> Damanhur -> Suez -> Alexandria -> Cairo
Cairo -> Alexandria -> Damanhur -> Suez -> Cairo
Cairo -> Alexandria -> Suez -> Damanhur -> Cairo
Cairo -> Suez -> Damanhur -> Alexandria -> Cairo
Cairo -> Suez -> Alexandria -> Damanhur -> Cairo
Calculating the Cost of Each Route Now, let's calculate the cost of each route using the given table:
Cairo -> Damanhur -> Alexandria -> Suez -> Cairo: 153 (Cairo to Damanhur) + 174 (Damanhur to Alexandria) + 144 (Alexandria to Suez) + 133 (Suez to Cairo) = 604 EGP
Cairo -> Damanhur -> Suez -> Alexandria -> Cairo: 153 (Cairo to Damanhur) + 182 (Damanhur to Suez) + 156 (Suez to Alexandria) + 167 (Alexandria to Cairo) = 658 EGP
Cairo -> Alexandria -> Damanhur -> Suez -> Cairo: 171 (Cairo to Alexandria) + 192 (Alexandria to Damanhur) + 182 (Damanhur to Suez) + 133 (Suez to Cairo) = 678 EGP
Cairo -> Alexandria -> Suez -> Damanhur -> Cairo: 171 (Cairo to Alexandria) + 144 (Alexandria to Suez) + 156 (Suez to Damanhur) + 143 (Damanhur to Cairo) = 614 EGP
Cairo -> Suez -> Damanhur -> Alexandria -> Cairo: 130 (Cairo to Suez) + 156 (Suez to Damanhur) + 174 (Damanhur to Alexandria) + 167 (Alexandria to Cairo) = 627 EGP
Cairo -> Suez -> Alexandria -> Damanhur -> Cairo: 130 (Cairo to Suez) + 156 (Suez to Alexandria) + 192 (Alexandria to Damanhur) + 143 (Damanhur to Cairo) = 621 EGP
Finding the Cheapest Route Comparing the costs, we find that the cheapest route is Cairo -> Damanhur -> Alexandria -> Suez -> Cairo, with a total cost of 604 EGP.
Final Answer The cheapest route to visit Damanhur, Alexandria, and Suez, starting and ending in Cairo, is Cairo -> Damanhur -> Alexandria -> Suez -> Cairo, with a total cost of 604 EGP.
Examples
Imagine you are a travel agent planning a trip for a client who wants to visit multiple cities in a specific order while minimizing travel costs. By analyzing different routes and their associated costs, you can determine the most economical itinerary. This problem demonstrates how optimization techniques can be applied to real-world travel planning to save money and time. Similar problems arise in logistics and supply chain management, where minimizing transportation costs is crucial for business efficiency. For example, a delivery company needs to find the most efficient route to deliver packages to multiple locations.
