Forecast sales for week $6$ using the na$$ve method, a simple average, and a three$-$period moving average.

$3.$ Hospitality Hotels forecasts monthly labor needs.

$($a$)$ Given the following monthly labor figures, make a forecast for June using a three$-$period moving average and a five$-$period moving average.

$\backslash$table$[[$Month$,$Actual Values$],[$January$,32],[$February$,41],[$March$,38],[$April$,39],[$May$,43]]$

$($b$)$ What would be the forecast for June using the na$$ve method?

$($c$)$ If the actual labor figure for June turns out to be $41,$ what would be the forecast for July using each of these models?

$($d$)$ Compare the accuracy of these models using the mean absolute deviation $($MAD$).$

$($e$)$ Compare the accuracy of these models using the mean squared error $($MSE$).$