Final answer:
To calculate the budgeted number of chests produced in January 2016, it is necessary to know January's sales figures, which are not provided in the question. With the given information, we can only determine that the desired ending inventory for January would be 4,800 units, but not the production number without January's sales data.
Step-by-step explanation:
The question requires us to calculate the budgeted number of chests produced in January 2016, given that the ending finished goods inventory for December is 3,000 units and ending finished goods are assumed to be 30 percent of the next month's sales. Knowing that the sales for April 2016 are expected to be 16,000 units, we can calculate January's production needs as follows:
First, we need to calculate the desired ending inventory for January. Since this should be 30 percent of February's sales and we do not have February's sales figures, we use April's sales as the next available month. Therefore, the desired ending inventory for January is 30 percent of 16,000 units, which equals 4,800 units.
Since the ending inventory of January is the beginning inventory of February, and we want to have 4,800 units at the end of January, plus we know that December's ending inventory (which is January's starting inventory) is 3,000 units, we can set up the following equation:
January production = (Ending inventory for January) - (Beginning inventory of January) + Sales for January
However, without the sales figure for January, we cannot calculate the exact number of chests to be produced in January. Thus, we would need more information to properly answer this question.