The inventory at June $1$ and costs charged to Work in Process$-$Department $60$ during June are as follows:

$3,800$ units, $70\%$ completed materials, $$43,400$ conversion$)$

$$77,400$

Direct materials, $30,000$ units

$360,000$

Direct labor

$244,000$

Factory overhead

$188,729$

Total cost to be accounted for

$$870,129$

During June, $30,000$ units were placed into production and $33,600$ units were completed, including those in inventory on June $1.$ On June $30,$ the inventory of work in process consisted of $200$ units that were $40\%$ completed. Inventories are costed by the FIFO method and all materials are added at the beginning of the process.

Determine the following, presenting your computations:

a$.$ Equivalent units of production for material and conversion cost

b$.$ Conversion cost per equivalent unit and material cost per equivalent unit

c$.$ Total cost of beginning work in process completed in the current period

d$.$ Total cost of work in process inventory at June $30$