$(($PLEASE ANSWER COMPLETELY. NOTE THAT THE QUESTION HAS $2$ PARTS$))))$ Fuqua Company$$s sales budget projects unit sales of part $198$Z of $11,000$ units in January, $12,100$ units in February, and $13,900$ units in March. Each unit of part $198$Z requires $4$ pounds of materials, which cost $4$ per pound. Fuqua Company desires its ending raw materials inventory to equal $40\%$ of the next month$$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 $31,2021.($a$)$Prepare a production budget for January and February $2022.($b$)$Prepare a direct materials budget for January $2022.$