$\begin{array}{cc}\text{P}\text{e}\text{r}\text{i}\text{o}\text{d}& \text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{V}\text{a}\text{l}\text{u}\text{e}\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}1& 294\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}2& 499\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}3& 437\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}4& 344\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}5& 335\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}6& 507\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}7& 529\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}8& 285\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}9& 433\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}10& 516\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}11& 501\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}12& 482\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}13& 280\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}14& 524\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}15& 515\\ \text{Q}\text{u}\text{a}\text{r}\text{t}\text{e}\text{r}16& 530\end{array}$

Use the attached Excel file with the quarterly demand $($in $1000$s of cases$)$ for a national beer distributor over the past $4$ years $.$

$1.$ Generate a forecast using Exponential smoothing, using $\backslash$alpha $=\mathrm{.}7.$ Assume forecast for Quarter $1($t $=1)$ was $294($i$.$e$.,$ F$1=294).(3$pts$)$

a$.$ What is the forecast for Quarter $17($t $=17)?$

b$.$ Find the MAD based on periods $5$ through $16($t $=5,6,...,16).$ What is the MAD?

c$.$ Use nonlinear programming to find the $\backslash$alpha that minimizes MAD.

i$.$ What is the $\backslash$alpha $?$

ii$.$ What is the MAD?

iii. What is the forecast for Quarter $17($t $=17)$ using this $\backslash$alpha $?$