$3-10.$ Underapplied overhead. Radium Corporation's current$-$year cost of goods sold is $$368,000,$ before any adjustment

for overapplied or underapplied manufacturing overhead. Sales revenues are $$580,000$ and selling and administrative

expenses are $$140,000.$ Radium applies manufacturing overhead to jobs using a predetermined overhead rate based on

machine hours. At the beginning of the year, Radium estimated that its manufacturing overhead costs for the year would

be $$170,000$ and that its machine hours for the year would be $25,000$ hours. Radium's actual manufacturing overhead

costs were $$163,400(4\%$ lower than estimate$)$ and its actual machine hours were lower than estimate$).$

a$.$ What is the amount of overapplied or underapplied overhead for the year?

b$.$ Assume that the difference between actual and applied overhead is immaterial. What is Radium's operating income?

c$.$ Now assume the difference between actual and applied overhead is material and that $$2,000$ of the difference is related

to units included in ending inventory $($ $$500$ in work in process and $$1,500$ in finished goods$)$ and the remainder is related

to units sold during the year. What is Radium's operating income?