Lily Company's sales budget projects unit sales of part $198Z$ of $11,000$ units in January, $12,600$ units in February, and $14,900$ units in March. Each unit of part $198Z$ requires $4$ pounds of materials, which cost $$2$ per pound. Lily Company desires its ending raw materials inventory to equal $40\%$ of the next month's production requirements, and its ending finished goods inventory to equal $20\%$ of the next month's expected unit sales. These goals were met at December $31,2024.$

$($a$)$

Prepare a production budget for January and February $2025.$