Question

you have three major routes to take to work. you can take tennessee street the entire way, you can take several back streets to work, or you can use the expressway. over the past two months, a friend has tried each route several times under different traffic conditions. this information is summarized in minutes of travel time to work in the following table. what route should you take to minimize travel time? use the ep criterion. probability of traffic no traffic congestion 0.3 mild traffic congestion 0.4 severe traffic congestion 0.3 tennessee street back roads expressway 15 20 30 30 25 30 45 35 30

Answer 1

To minimize travel time, the Expected Value for each route is calculated by multiplying the time taken for each traffic condition by its probability and adding these products together. The Back Roads route has the lowest expected travel time at 26.5 minutes, making it the best choice based on the EV criterion.

Step-by-step explanation:

To determine which route to take to minimize travel time using the Expected Value (EV) criterion, we need to perform some calculations. First, we multiply the time taken for each traffic condition by its probability and then add all these products together for each route. This will give us the expected travel time for each route.

Tennessee Street:

• 
  
• No traffic: 15 minutes * 0.3 probability = 4.5 minutes
• 
  
• Mild traffic: 30 minutes * 0.4 probability = 12 minutes
• 
  
• Severe traffic: 45 minutes * 0.3 probability = 13.5 minutes

Expected travel time for Tennessee Street = 4.5 + 12 + 13.5 = 30 minutes

Back Roads:

• 
  
• No traffic: 20 minutes * 0.3 probability = 6 minutes
• 
  
• Mild traffic: 25 minutes * 0.4 probability = 10 minutes
• 
  
• Severe traffic: 35 minutes * 0.3 probability = 10.5 minutes

Expected travel time for Back Roads = 6 + 10 + 10.5 = 26.5 minutes

Expressway:

• 
  
• No traffic: 30 minutes * 0.3 probability = 9 minutes
• 
  
• Mild traffic: 30 minutes * 0.4 probability = 12 minutes
• 
  
• Severe traffic: 30 minutes * 0.3 probability = 9 minutes

Expected travel time for Expressway = 9 + 12 + 9 = 30 minutes

Based on these calculations, the Back Roads route has the lowest expected travel time, and so, according to the EV criterion, it should be the chosen route to minimize travel time to work.