Below is the sales data for Forever Young Boutique between March of Year $1$ and July of

Year $5.($You can find the Excel sheet

containing this

Year $2$

$6381\mathrm{.}074405\mathrm{.}839126\mathrm{.}9510970\mathrm{.}4510189\mathrm{.}287043\mathrm{.}856717\mathrm{.}379139\mathrm{.}7211315\mathrm{.}1910838\mathrm{.}411150\mathrm{.}94$

data on Blackboard.$)$

$1)$ Develop a forecast for the sales in August of Year $5$ by using three different forecasting techniques: Three$-$month simple moving average, Weighted moving average with weights $0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}2($the weight $0\mathrm{.}5$ is given to the most recent observation$),$ and Exponential smoothing method with a smoothing constant of $0\mathrm{.}3.(15$ points$)$

$2)$ Which forecasting method you considered in Question $1$ is the most accurate according to the Mean Absolute Deviation $($MAD$)$ criterion? Please justify your answer. $(5$ points$)$