PROBLEM 1 [15 pts] 1.1. Jenna and Greg plan to go on a hiking trip. On September 24th, they open their Google Calendars, and look through their work schedules. It seems like there are only two options: *1 = go on October 24" (i.e., in one month) and stay for 2 days * = go on November 24" (i.e., in two months) and stay for 5 days (use month as unit time) a) Jenna is a discounted utility maximizer with 8 = 0.7. V(n days hiking trip) = log (n) Given this information, which option would Jenna choose? Show your math. [2.5 pts] b) Greg is a beta-delta utility maximizer with 6 = 0.6 and B = 0.5. V(n days hiking trip) = log .(n) Given this information, which option would Greg choose? Show your math. [2.5 pts]1.2. In one month, on October 24", they decide to reevaluate their choice and consider the initial two dates again: *1 = go on October 24" (i.e., today) and stay for 2 days *2 = go on November 24" (i.e., in one month) and stay for 5 days a) Would Jenna shift her initial preference? Show your math. [2.5 pts] b) Would Greg shift his initial preference? Show your math. [2.5 pts]