$-4,$ Accessory World makes floor mats for the automobile industry. Finished sets of mats must pass through two departments: Cutting and Coating. Large sheets of synthetic material are cut to size in the Cutting Department and then transferred to the Coating Department, where each set is sprayed with a chemical coating for improved durability. The following information pertains to May activity in the Cutting Department.

Cost data:

Total cost of beginning inventory on May $1$

Direct materials costs incurred in May

Conversion costs incurred in May

Physical units data:

Units in process, May $1$

Units started in May

$q,$

Units in process, May $31q,$

Percentage of completion data:

Direct materials, May $1q,$

Conversion, May $1q,$

Direct materials, May $31q,$

Conversion, May $31q,$

$

$44,800$

$200,000$

$87,200$

$8,000$ sets

$50,000$ sets

$10,000$ sets

$100\%$

$80$

$100\%$

$20$

a$.$ Prepare a schedule showing: $(1)$ the number of mat sets transferred from the Cutting Department to the Coating Department in May, and $(2)$ the number of mat sets started and completed by the Cutting Department in May.

b$.$ Compute the equivalent units of input resources for the Cutting Department in May.

c$.$ Compute the cost per equivalent unit of input resource for the Cutting Department in May.

d$.$ Prepare the summary journal entry required to transfer the cost of completed mat sets from the Cutting Department to the Coating Department in May.

e$.$ Compute the total cost assigned to the Cutting Department's ending inventory on May $31.$