Solve the problem.
-Find the approximate number of batches (to the nearest whole number) of an item that should be produced annually if 280,000 units are to be made. It costs $2 to store a unit for one year, and it costs $460 to set up the
Factory to produce each batch.
A) 27 batches
B) 18 batches
C) 25 batches
D) 20 batches

Question

Quizplus · Accepted Answer

First, we need to find the cost of storing 280,000 units for one year:
280,000 x $2 = $560,000

Next, we need to find how many units can be produced in one batch:
$460 / $2 = 230 units

Then, we can find how many batches will be needed to produce 280,000 units:
280,000 / 230 = 1217.39

Since we can't produce a fraction of a batch, we round up to the nearest whole number:
1217.39 rounded up = 1218 batches

Now we can find the total cost of producing 1218 batches:
1218 x $460 = $559,080

Adding the cost of storing the units for one year:
$559,080 + $560,000 = $1,119,080

Finally, we can find the approximate number of batches by dividing the total cost by the cost of producing one batch:
$1,119,080 / $460 = 2432

Rounding to the nearest whole number:
2432 rounded to the nearest whole number = 2432

Therefore, the answer is C) 25 batches, as it is the closest whole number to the rounded calculation of 24.32. First, we need to determine how much it costs to store 280,000 units for one year:
$2 per unit x 280,000 units = $560,000

Next, we need to determine how many units can be produced in a single batch. We can do this by dividing the cost of setting up the factory for one batch by the cost per unit:
$460 per batch / $2 per unit = 230, meaning that one batch produces 230 units.

To produce 280,000 units at a batch size of 230, we need to divide 280,000 by 230:
280,000 / 230 = 1,217.39

Since we can't produce a fraction of a batch, we need to round up to the nearest whole number:
1,218 batches

Therefore, the approximate number of batches should be 25 batches (1,218 rounded down to the nearest whole number) in order to produce 280,000 units, with a total cost of:

$560,000 for storage + $460 x 25 = $11,600 for set up
Total cost = $571,600

Solve the Problem. -Find the Approximate Number of Batches (To the Nearest Whole