Cullumber Company produces and sells automobile batteries, the heavy$-$duty HD$-240.$ The $2022$ sales forecast is as follows.

$\backslash$table$[[$Quarter$,$HD$-240],[1,4,200],[2,5,880],[3,6,720],[4,8,400]]$

The January $1,2022,$ inventory of HD$-240$ is $1,680$ units. Management desires an ending inventory each quarter equal to $40\%$ of the next quarter's sales. Sales in the first quarter of $2023$ are expected to be $25\%$ higher than sales in the same quarter in $2022.$

Prepare quarterly production budgets for each quarter and in total for $2022.$