Question $9.$ A company would like to develop a short$-$term forecasting model for its retail operations and is focusing on the exponential smoothing and moving average methods. The actual data for the last six periods for an operation are: $($see image$)$

$9$a$)(4$ points$)$ Implement Exponential Smoothing with alpha$=1//2$ and forecast the number of units for Week

What is the forecast for week $7?$

$9$b$)(2$ points$)$ What is the MAD for this method?

$9$c$)(4$ points$)$ implement a $3-$Period Moving Average and forecast the number of units for Week $7.$ What is the forecast for week $7?$

$9$d$)(2$ points$)$ What is the MAD for this method?

$9$e$)(3$ points$)$ Which of these methods performs better for the company? $(1$ point$)$ Why? $(2$ points$)$

$9$f$)(4$ points$)$ Using the MA$(3)$ forecast, if the company wanted to achieve a $90\%$ service level, how much should they order for week $7?$

Z value: $0\mathrm{.}00\mathrm{.}4330\mathrm{.}6751\mathrm{.}041\mathrm{.}281\mathrm{.}652\mathrm{.}32$

Probability: $50\%66\mathrm{.}7\%75\%85\%90\%95\%99\%$