What is the forecast for May based on a weighted moving average applied to the following past demand data and using the weights: $4,3,3($largest weight is for most recent data$)?$

$\backslash$table$[[$Nov$.,$Dec.,Jan.,Feb.,Mar.,April$],[37,36,40,42,47,43]]$

A coffee chain sells temperature$-$controlled smart mugs at $$150$ each. The monthly sales of mugs for the last twelve months were:

$\backslash$table$[[$Month$,$Sales$],[$January$,825],[$February$,756],[$March$,808],[$April$,950],[$May$,678],[$June$,875],[$July$,695],[$August$,589],[$September$,690],[$October$,890],[$November$,1030],[$December$,1525]]$

$($a$)$ Compute a $3-$month moving average demand forecast for each month from June through December. $($Round all forecasts to the nearest whole unit.$)$

$($b$)$ Compute a $5-$month moving average demand forecast for each month from June through December. $($Round all forecasts to the nearest whole unit.$)$