The following information is available for Carter Corporation:

Materials inventory decreased $$4,000.$

Materials inventory on December $31$ was $50\%$ of materials inventory on January $1.$

Beginning work in process inventory was $$145,000.$

Ending finished goods inventory was $$65,000.$

Purchases of direct materials were $$154,700.$

Direct materials used were $2\mathrm{.}5$ times the cost of direct labor.

Total manufacturing costs incurred were $$246,400,$ which is $80\%$ of cost of goods manufactured and $$156,000$ less than cost of goods sold.

Note to students: The answers are not necessarily calculated in alphabetical order.

a$.$ Compute finished goods inventory on January $1.$

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b$.$ Compute work in process inventory on December $31.$

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c$.$ Compute direct labor incurred.

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d$.$ Compute factory overhead incurred.

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e$.$ Compute materials inventory on January $1.$

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f$.$ Compute materials inventory on December $31.$

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g$.$ Compute direct materials used.