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%u2019s equivalent units of production with respect to direct materials under each of three separate assumptions using the weighted-average method for process costing:

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