Carter, Inc. uses a traditional volume$-$based costing system in which direct labor hours are the allocation base. Carter produces two different products: Product A$,$ which uses $100,000$ direct labor hours, and Product B$,$ which uses $300,000$ direct labor hours. Carter is considering switching to an ABC system by splitting its manufacturing overhead cost of $$1,020,000$ across three activities: Design, Production, and Inspection. Under the traditional volume$-$based costing system, the predetermined overhead rate is $$2\mathrm{.}55/$direct labor hour. Under the ABC system, the cost of each activity and proportion of the activity drivers used by each product are as follows:

Total Cost Proportion used by Product A Proportion used by Product B

Design $($Engineering Hours$)$ $ $200,00025\%75\%$

Production $($Direct Labor Hours$)$ $ $600,00025\%75\%$

Inspection $($Batches$)$ $ $220,00075\%25\%$

Required:

a$.$ Calculate the indirect manufacturing costs assigned to Product A under the traditional costing system.

b$.$ Calculate the indirect manufacturing costs assigned to Product B under the traditional costing system.

c$.$ Calculate the indirect manufacturing costs assigned to Product A under the ABC system.

d$.$ Calculate the indirect manufacturing costs assigned to Product B under the ABC system.

e$.$ Which product is under$-$costed and which is over$-$costed under the volume$-$based cost system compared to ABC?