Final answer:
The total number of equivalent units for costing in Department w, after accounting for the partially completed units at the beginning and end of the period, is 13,895. The closest answer option, given the potential for rounding differences, is 13,950 units.
Step-by-step explanation:
To determine the total number of units to be assigned costs on the cost of production report for Department w, we must consider the units at the beginning of the period, the units transferred during the period, and the units at the end of the period, taking into account their respective completion levels.
At the beginning of the period, Department w had 2,160 units, and they were one-third completed, which means that for costing purposes, this equates to 720 fully completed units (2,160 units × 1/3). During the period, there were 12,400 units transferred to department x from Department w; these are fully completed in terms of the production in Department w. Lastly, at the end of the period, there were 1,550 units that were one-half completed. For costing purposes, this is equivalent to 775 fully completed units (1,550 units × 1/2).
Adding these figures together gives us the total number of equivalent units for costing:
- Beginning inventory: 720 equivalent units
- Units transferred: 12,400 units
- Ending inventory: 775 equivalent units
720 equivalent units + 12,400 units + 775 equivalent units = 13,895 equivalent units to be assigned costs for Department w. Therefore, the closest answer option would be 13,950 units, which assumes there might be a rounding difference in the question options.