Cooperative San Latino of southern Sonora state in Mexico makes a unique syrup using cane sugar and local herbs. The syrup is sold in small bottles and is prized as a flavouring for drinks and desserts. The bottles are sold for $$20$ each. $($The Mexican currency is the peso, denoted by $$.)$ The first stage in the production process is carried out in the Mixing department, which removes foreign matter from the raw materials and mixes the raw materials in the proper proportions in large vats. The company uses the weighted average cost method in its process costing system.

A hastily prepared report for the Mixing department for May follows:

Quantity Schedule

Units to be accounted for:

Work in process, May $1(70\%$ materials, $80\%$ conversion cost added last month$)17,200$

Started into production $193,800$

Total units $211,000$

Units accounted for as follows:

Transferred to the next department $185,500$

Work in process, May $31(75\%$ materials, $80\%$ conversion cost added this month$)25,500$

Total units $211,000$

Total Cost

Cost to be accounted for:

Work in process, May $1$ $ $111,500$

Cost added during the month $878,000$

Total cost $ $989,500$

Cost Reconciliation

Cost accounted for as follows:

Transferred to the next department $ $864,000$

Work in process, May $31125,500$

Total cost $ $989,500$

Cooperative San Latino has just been acquired by another company, and the management of the acquiring company wants some additional information about Cooperative San Latino$$s operations.

Required:

$1.$ What were the equivalent units for the month?

$2.$ What were the costs per equivalent unit for the month? The beginning inventory consisted of the following costs: materials, $$67,200$; conversion cost, $$32,200.$ The costs added during the month consisted of materials, $$622,000$; conversion cost, $$278,000.($Round your answers to $3$ decimal places.$)$

$3.$ How many of the units transferred to the next department were started and completed during the month?