EX $9-23($Algo$)$ Budgeting Production and Direct$-$Material Purchases $($LO $9-3,9-6)$

Bodin Company budgets on an annual basis. The following beginning and ending inventory levels $($in units$)$ are plannned for the year $20$x$1.$ Five units of raw material are required to produce each unit of finished product.

January $1$ December $31$

Raw material $37,00050,000$

Work in process $16,00016,000$

Finished goods $87,00063,000$

Required:

If Bodin Company plans to sell $454,000$ units during the year, compute the number of units the firm would have to manufacture during the year.

If $510,000$ finished units were to be manufactured by Bodin Company during the year, determine the amount of raw material to be purchased.

Please demonstrate algebraically how the second question is solved, step by step.