You can choose to visit these cities in any order, but you will start and end your trip in Jerusalem. If you have a budget of NIS 900, which of the following routes are possible?

I. Jerusalem [tex]\rightarrow[/tex] Tel Aviv [tex]\rightarrow[/tex] Ra'anana [tex]\rightarrow[/tex] Holon [tex]\rightarrow[/tex] Jerusalem
II. Jerusalem [tex]\rightarrow[/tex] Holon [tex]\rightarrow[/tex] Tel Aviv [tex]\rightarrow[/tex] Ra'anana [tex]\rightarrow[/tex] Jerusalem
III. Jerusalem [tex]\rightarrow[/tex] Ra'anana [tex]\rightarrow[/tex] Tel Aviv [tex]\rightarrow[/tex] Holon [tex]\rightarrow[/tex] Jerusalem

a. II only
b. I and II
c. I and III
d. None of these are possible.

Among the routes starting and ending in Jerusalem, Routes II (Holon, Tel Aviv, Ra'anana) and III (Ra'anana, Tel Aviv, Holon) are possible within the budget of NIS 900. Route I exceeds the budget at 805 NIS, while Routes II and III are within the budget at 727 NIS and 758 NIS, respectively. Thus, the answer is b. I and II .
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Answered by Anonymous | 2025-07-04

Calculate the cost of Route I: Jerusalem → Tel Aviv → Ra'anana → Holon → Jerusalem, which is 805 NIS.
Calculate the cost of Route II: Jerusalem → Holon → Tel Aviv → Ra'anana → Jerusalem, which is 727 NIS.
Calculate the cost of Route III: Jerusalem → Ra'anana → Tel Aviv → Holon → Jerusalem, which is 758 NIS.
Determine that routes II and III are possible since their costs are less than or equal to the budget of 900 NIS. The answer is therefore c . I an d III ​ .

Explanation

Problem Analysis We are given the distances between several cities and a budget of NIS 900. We need to determine which of the given routes, starting and ending in Jerusalem, are possible within the budget. A route is possible if the total cost of the route is less than or equal to NIS 900.

Calculating Route Costs Let's calculate the cost of each route:


Route I: Jerusalem → Tel Aviv → Ra'anana → Holon → Jerusalem Cost = (Jerusalem to Tel Aviv) + (Tel Aviv to Ra'anana) + (Ra'anana to Holon) + (Holon to Jerusalem) Cost = 234 + 203 + 218 + 150 = 805 NIS
Route II: Jerusalem → Holon → Tel Aviv → Ra'anana → Jerusalem Cost = (Jerusalem to Holon) + (Holon to Tel Aviv) + (Tel Aviv to Ra'anana) + (Ra'anana to Jerusalem) Cost = 150 + 198 + 203 + 176 = 727 NIS
Route III: Jerusalem → Ra'anana → Tel Aviv → Holon → Jerusalem Cost = (Jerusalem to Ra'anana) + (Ra'anana to Tel Aviv) + (Tel Aviv to Holon) + (Holon to Jerusalem) Cost = 176 + 234 + 198 + 150 = 758 NIS

Comparing with Budget Now, let's compare the cost of each route with the budget of NIS 900:

Route I: 805 NIS > 900 NIS (Not possible) Route II: 727 NIS ≤ 900 NIS (Possible) Route III: 758 NIS ≤ 900 NIS (Possible)

Determining Possible Routes Therefore, routes II and III are possible within the budget.

Final Answer The possible routes are II and III.


Examples
Understanding route costs is crucial in logistics and transportation. For example, a delivery company needs to determine the most cost-effective routes for its drivers to minimize expenses while ensuring timely deliveries. By analyzing different routes and their associated costs, the company can optimize its operations and improve profitability. This involves calculating distances, fuel consumption, and other relevant factors to make informed decisions about route selection. Similarly, in urban planning, understanding the costs associated with different transportation routes helps in designing efficient public transportation systems and managing traffic congestion.

Answered by GinnyAnswer | 2025-07-04