The following information is taken from the accounts of Latta Company. The entries in the T$-$accounts are summaries of the transactions that affected those accounts during the year.

Manufacturing Overhead

Debit Credit

$($a$)463,104($b$)385,920$

Balance $77,184$

Work in Process

Debit Credit

Balance $20,080($c$)714,000$

$263,500$

$85,500$

$($b$)385,920$

Balance $41,000$

Finished Goods

Debit Credit

Balance $49,000($d$)642,000$

$($c$)714,000$

Balance $121,000$

Cost of Goods Sold

Debit Credit

$($d$)642,000$

The overhead that had been applied to production during the year is distributed among Work in Process, Finished Goods, and Cost of Goods Sold as of the end of the year as follows:

Work in Process, ending $ $19,680$

Finished Goods, ending $58,080$

Cost of Goods Sold $308,160$

Overhead applied $ $385,920$

For example, of the $$41,000$ ending balance in work in process, $$19,680$ was overhead that had been applied during the year.

Required:

$1.$ Identify reasons for entries $($a$)$ through $($d$).$

$2.$ Assume that the underapplied or overapplied overhead is closed to Cost of Goods Sold. Prepare the necessary journal entry.

$3.$ Assume that the underapplied or overapplied overhead is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold. Prepare the necessary journal entry.