a$)$ When might a manager prefer a linear trend technique to a moving average technique and why? $(5$ points$)$

A local theatre company in St$.$ John's has had the following sales revenue for the past $5$ years:

$\backslash$table$[[$Year$,$Revenue $($$$000\text{'}$s$)],[2019,5,900],[2020,6,100],[2021,5,800],[2022,6,200],[2023,5,700]]$

b$)$ Calculate forecasts for $2019-2023$ using Linear$-$Trend Equation and Trend Adjusted Exponential Smoothing $($or double$-$exponential smoothing$)$ methods. Use an $=0\mathrm{.}25$ and $=0\mathrm{.}5($start with initial estimates $S_{2019}=$$$6,000,T_{2019}=$$$200).(15$ points$)$

c$)$ Calculate MAPE for $2019-2023$ for each method and indicate which method provides the better forecasts; state any necessary assumptions. Explain. $(8$ points$)$

d$)$ Forecast revenue for $2024$ and $2025$ based on your preferred method from b$).$ State any necessary assumptions. $(2$ points$)$