In its first month of operations (May of 2019), Allred Company's Department 1 incurred charges of \($72,000\) for direct materials (9,000 units), \($38,700\) for direct labor, and \($13,500\) for manufacturing overhead. At month-end, 8,500 units had been finished and transferred out. Those units remaining were finished with respect to materials but only 40% finished with respect to conversion. Assuming Allred uses the FIFO method and that materials are added at the beginning of the process and conversion costs are incurred evenly throughout the period, compute the following:

a. The equivalent units for materials and conversion costs.

b. The cost per equivalent unit for materials and conversion costs.

c. The total cost assigned to the units transferred out.

d. The total cost assigned to the ending inventory.

e. Prove that your solutions to requirements (c) and (d) sum to the total costs to be accounted for.