Problem $3-22($Algo$)$

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past $10$ months. The forecasts and actual sales are as follows:

Month Sales Forecast $1$ Forecast $2$

$1840820795$

$2850820795$

$3830805845$

$4810815850$

$5780815785$

$6840775811$

$7800795785$

$8835810835$

$9790780830$

$10825820855$

a$.$ Compute the MSE and MAD for each forecast. $($Round your answers to $2$ decimal places.$)$

b$.$ Compute MAPE for each forecast. $($Round your intermediate calculations to $5$ decimal places and final answers to $4$ decimal places.$)$

c$.$ Prepare a naive forecast for periods $2$ through $11$ using the given sales data. Compute each of the following; $(1)$ MSE, $(2)$ MAD, $(3)$ tracking signal at month $10,$ and $(4)2$s control limits$.($Negative values should be indicated by a minus sign. Round your answers to $2$ decimal places.$)$