$(30$ points$)$ The data on sheet Q$1$ provides information on the demand for a product over a period of $90$ days. Use this data to evaluate the following forecasting models:

$(\backslash$alpha $=0\mathrm{.}25,\backslash$delta $=0\mathrm{.}0)$

$(\backslash$alpha $=0\mathrm{.}25,\backslash$delta $=0\mathrm{.}2)$

$(\backslash$alpha $=0\mathrm{.}25,\backslash$delta $=0\mathrm{.}4)$

$(\backslash$alpha $=0\mathrm{.}45,\backslash$delta $=0\mathrm{.}1)$

$(\backslash$alpha $=0\mathrm{.}45,\backslash$delta $=0\mathrm{.}3)$

$(\backslash$alpha $=0\mathrm{.}45,\backslash$delta $=0\mathrm{.}5)$

For all the models, assume that the Forecast without trend for day $1$ is the same as the actual demand $(4917$ units$)$ and the value of trend for day $1$ is $0.$

Compute the Mean Absolute Percent Error for all six models and provide the information in the table below:

Model MAPE

$\backslash$alpha $\backslash$delta

$0\mathrm{.}250\mathrm{.}0$

$0\mathrm{.}250\mathrm{.}2$

$0\mathrm{.}250\mathrm{.}4$

$0\mathrm{.}450\mathrm{.}1$

$0\mathrm{.}450\mathrm{.}3$

$0\mathrm{.}450\mathrm{.}5$

Based on your results above:

Which model would you choose to predict this data? Provide a brief explanation for your choice.

Using the model that you chose as your best model $($from part $($a$)),$ what is your forecast for day $91?$

Would you consider the data to have no trend, weak trend, medium trend, or strong trend? Provide an explanation for your answer.