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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]1.3. Assume that on September 24" Jenna and Greg have the option commit or not to commit to the choice they made on this date. If they chose to commit and rent a car, they would not have the option to change their minds on October 24" and they would go with whichever option they picked initially. If they chose not to commit, they would revisit their decision on October 24" and could change their minds on this date. Assuming that both Jenna and Greg are aware of the stability/instability in their choices, which option would each pick? Explain why. [2 pts]