Sure, let's break down the solution step by step.
### Part 1: Beginning Balance in the 3rd Processing Department
First, let's find the beginning balance in the 3rd processing department using the given data.
We have the following information:
- Transfer from 2nd Department: [tex]$1,000,000
- January costs: $[/tex]200,000
- Total Debits: [tex]$1,300,000
- Ending Balance: $[/tex]600,000
We know that:
[tex]\[ \text{Total Debits} = \text{Beginning Balance} + \text{Transfers from 2nd Dept.} + \text{January Costs} \][/tex]
From the given data:
[tex]\[ 1,300,000 = \text{Beginning Balance} + 1,000,000 + 200,000 \][/tex]
Solving for the beginning balance:
[tex]\[ \text{Beginning Balance} = 1,300,000 - 1,000,000 - 200,000 \][/tex]
[tex]\[ \text{Beginning Balance} = 100,000 \][/tex]
So, the beginning balance in the 3rd processing department is [tex]$100,000.
### Part 2: Cost of Goods Sold (COGS)
We also need to find the Cost of Goods Sold (COGS) given the inventory information.
We have the following information:
- Beginning Inventory of Finished Goods: $[/tex]200,000
- Ending Inventory of Finished Goods: [tex]$300,000
- Goods Manufactured: $[/tex]800,000 (assumed to be part of the given data)
The formula for COGS is:
[tex]\[ \text{COGS} = \text{Beginning Inventory} + \text{Goods Manufactured} - \text{Ending Inventory} \][/tex]
Plugging the values into the formula:
[tex]\[ \text{COGS} = 200,000 + 800,000 - 300,000 \][/tex]
[tex]\[ \text{COGS} = 700,000 \][/tex]
So, the Cost of Goods Sold (COGS) is [tex]$700,000.
### Summary
- The beginning balance in the 3rd processing department is $[/tex]100,000.
- The Cost of Goods Sold (COGS) is $700,000.
