Antoine Machining estimated its manufacturing overhead to be $$296,960$ and its direct materials costs to be $$464,000$ in Year $1.$ Three of the jobs that Antoine Machining worked on in Year $1$ had actual direct materials costs of $$29,000$ for Job AM$002,$ $$69,000$ for Job AM$005,$ and $$84,000$ for Job AM$008.$ For Year $1,$ actual manufacturing overhead was $$320,000$ and total direct materials cost was $$554,000.$ Manufacturing overhead is applied to jobs on the basis of direct materials costs using predetermined rates.

Required:

a$.$ How much overhead was assigned to each of the three jobs, AM$002,$ AMO$05,$ and AM$008?$

b$.$ What was the over$-$ or underapplied manufacturing overhead for Year $1?$