The production department in a process manufacturing system completed 191,500 units of product and transferred them to finished goods during a recent period. Of these units, 31,500 were in process at the beginning of the period. The other 160,000 units were started and completed during the period. At period-end, 29,500 units were in process. Compute the department's equivalent units of production with respect to direct materials under each of three separate assumptions:

1. All direct materials are added to products when processing beings.

2. Direct materials are added to products evenly throughout the process. Beginning goods in process inventory was 40% complete and ending goods in process inventory was 75% complete.

3. One-half of direct materials is added to products when the process begins and the other half is added when the process is 75% complete as to direct labor. Beginning goods in process inventory is 40% complete as to direct labor, and ending goods in process inventory is 60% complete as to direct labor.