Previous note: The statement is not clear at some relevant points so i
make some assumptions that are clarified in the answer, if one of
these assumptions are incorrect, resulting in a misinterpretation of
the problem's statement, please clarify the point using the request of
an answer clarification feature; I will correct the calculations
according with the new info.
1. Cost of direct materials:
The 20% of the source good is discarded (1 of 5 quarts), and 80% is
accepted (4 of 5 quarts); so to get 6 good quarts to do a single batch
the company must purchase 6 / 0.8 = 7.5 quarts.
At $0.80 per quart, the cost per batch of source good is:
7.5*0.8 = $6.00
According to the statement other materials costs are $.45 per gallon,
that is a total cost of $4.50 for each 10 gallon batch.
Then the cost due direct material per 10 gallon batch is $10.50.
2. Direct labor cost:
Assuming that the 3 minutes at statement refers to the labor time
needed to sort 1 quart of source material from the mix of good and bad
material; and knowing that 6 quarts are needed to produce single
batch, then 18 minutes are spent in sorting.
12 minutes of direct labor time are required to process each batch.
Then 30 minutes of direct labor are needed to produce each batch.
Since the cost per hour of direct labor is $9, then the cost for a 10
gallon batch is $4.50 .
3. Packaging cost:
I am assuming that the total cost of material and labor of packaging
is $.41 per quart.
A 10 gallon batch has 40 quarts which, at $.41 per quart, amounts to a
packaging cost of $16.40 per batch.
Then the total cost of a 10 gallon batch is:
Direct materials + Direct labor + Packaging = $10.5 + $4.5 + $16.4 =
To produce a single 10 gallon batch costs $31.40 .
I hope that this helps you. Fell free to request for a clarification
if you find something unclear or if one of my assumptions are not