On January $1,2022,$ the Sheffield Company budget committee has reached agreement on the following data for the $6$ months ending June $30,2022.$

Sales units:

Ending raw materials inventory:

Ending finished goods inventory:

Third$-$quarter production:

First quarter $6,500$; second quarter $7,800$; third quarter $9,100.$

$40\%$ of the next quarter's production requirements.

$25\%$ of the next quarter's expected sales units.

$9,360$ units.

The ending raw materials and finished goods inventories at December $31,2021,$ follow the same percentage relationships to production and sales that occur in $2022.$ Three pounds of raw materials are required to make each unit of finished goods. Raw materials purchased are expected to cost $$4$ per pound.

$($a$)$

Prepare a production budget by quarters for the $6-$month period ended June $30,2022.$