Mullen Magic Shows is evaluating attendance at the shows and planning whether to train more magicians. They have the following data:
Year Total Audience
2013 97130
2014 101326
2015 96956
2016 99816
2017 99694
2018 103762
2019 104958
2020 110988
2021 112157
2022 110370
a) Plot these data, develop a hypothesis of an appropriate model, estimate the model's parameters, and forecast passengers for 2023-2025.
b) Illustrate an exponential smoothing model using an alpha of .1 and then an alpha of .5.
c) In doing some analysis, they assume each show has about 500 attendees. Each magician they hire can work up to 50 shows a year and is paid $1500 per show up to 50 shows.
Recently, magicians complained that they are under contract for 50 shows but only paid for shows they work. If each magician is paid $500 per show she/he does not work, what does this policy cost per year?