FC$.62$ Mitchell's Mills is a startup looking to break into the preparedness market with a revolutionary new wheat grinder called the WG$1.$ Since Mitchell's is a new company they do not have any historical data for sales of its flagship product, but they estimate they will be able to sell $456$ in the month of April. The table below contains actual sales data for April and each of the succeeding five months $($through September$)$:

Suppose it was the beginning of May and you were asked to develop a forecast for the month of May. Your only actual sales data was for the month of April. Because of this paucity of data you decide to use the exponential smoothing method for the construction of your forecasting model. You determine that an alpha value of $0\mathrm{.}75$ would be appropriate.

Based on the above information, what would have been your forecast for the month of May? $($Display your answer to two decimal places.$)$

If you follow this same forecasting process through all the months, continuing with June and going through September, what would be the forecast in the month of September? $($Display your answer to two decimal places.$)$

What is the MAD for this forecast $($based on six months of forecasts$-$April through September$)?($Display your answer to two decimal places.$)$

What is the MAPE for this forecast $($based on six months of forecasts$-$April through September$)?($Write your answer as a percentage, and display your answer to two decimal places.$)$