Suppose you live in Delmar and commute to UCSD for class everyday. You typically use I-5 for your commute and you estimate that the commute time varies between 15 and 30 minutes depending on the traffic. Assume that the commute time is either 15 minutes with 50% likelihood or 30 minutes with 50% likelihood.

Your friend tells you Torrey Pines Rd never has traffic problems, and that if you use it, your commute will take exactly 20 minutes. Suppose you want to minimize the expected commute time.

a. Which of these two routes would you pick for your commute (i.e., would you stick to using I-5 or would you switch to using the Torrey Pines Rd?)? (1.5 pts)

b. What is the expected duration of your commute? [Assume that you don't know how the traffic looks when you are choosing your route] (0.5 pt)

Your roommate has had enough of you complaining about the San Diego traffic, and gets you a GPS device with live traffic update. You decide on the following more flexible routing strategy for your future commutes - if your GPS tells you that the traffic on I-5 is okay (with 50% likelihood), you will use I-5 and reach UCSD in 15 minutes; however, if the GPS says that traffic looks bad on I-5 (with 50% likelihood), you will take Torrey Pines Rd and reach UCSD in 20 minutes.

c.What is the new expected duration of your commute? (1.5 pts)

d. How much time on average did using the GPS save you (compared to not using the GPS)? (0.5 pt)