Final answer:
To meet the company's goals, the production in January 2017 should be 284,800 units.
Step-by-step explanation:
To calculate how many units should be produced in January 2017, we first need to calculate the desired ending inventory for February 2017. Since the company wants the ending inventory to be equal to 30% of the next month's budgeted unit sales, the desired ending inventory for February 2017 is 30% of 310,000 units, which is 93,000 units.
Next, we need to calculate the difference between the desired ending inventory and the units on hand on December 31, 2016. The difference is 93,000 - 82,200 = 10,800 units.
To meet the company's goals, the production in January 2017 should be the sum of budgeted unit sales for January 2017 and the difference calculated above. Therefore, the number of units that should be produced in January 2017 is 274,000 + 10,800 = 284,800 units.