Budgeted direct materials purchases for the third quarter would be:

Steps to Solve

1. Calculate Direct Material Requirements for Quarter 3

To find the total amount of direct materials required for the third quarter, multiply the planned production by the amount of material required per unit.
The production for Quarter 3 is 34,000 units, and each unit requires 3 pounds of direct material.

$$ \text{Direct Material Requirements} = \text{Units} \times \text{Pounds per Unit} = 34,000 \times 3 = 102,000 \text{ pounds} $$

2. Determine Ending Inventory for Quarter 3

The ending inventory for Quarter 3 should be equal to 30% of the next quarter's (Quarter 4) direct material requirements.
First, find the requirements for Quarter 4:

The planned production for Quarter 4 is 48,000 units, which requires:

$$ \text{Direct Material Requirements for Quarter 4} = 48,000 \times 3 = 144,000 \text{ pounds} $$

Now, calculate 30% of this amount:

$$ \text{Ending Inventory for Quarter 3} = 0.3 \times 144,000 = 43,200 \text{ pounds} $$

3. Calculate Beginning Inventory for Quarter 3

The beginning inventory for Quarter 3 is the ending inventory from Quarter 2.
First, we find the direct material requirements for Quarter 2, which is 38,000 units:

$$ \text{Direct Material Requirements for Quarter 2} = 38,000 \times 3 = 114,000 \text{ pounds} $$

Then calculate the ending inventory for Quarter 2:

$$ \text{Ending Inventory for Quarter 2} = 0.3 \times 114,000 = 34,200 \text{ pounds} $$

Thus,

$$ \text{Beginning Inventory for Quarter 3} = 34,200 \text{ pounds} $$

4. Calculate Direct Material Purchases for Quarter 3

Now we can calculate the direct materials purchases for Quarter 3 using the formula:

$$ \text{Purchases} = \text{Direct Material Requirements} + \text{Ending Inventory} - \text{Beginning Inventory} $$

Substituting the values we calculated:

$$ \text{Purchases} = 102,000 + 43,200 - 34,200 = 111,000 \text{ pounds} $$