Lincolnshire Lumber sells boards for many uses including wood floors. For floors, the boards are sold to local installers or do$-$it$-$yourself homeowners. The boards go through up to four processes, although only the first two are completed for all sales.

Lincolnshire employs $10$ workers in the Flooring Department who are each trained and experienced in all four processes. Each employee works $35$ hours per week for $50$ weeks per year. Lincolnshire allocates $10$ percent of the workers' time to training and staff meetings, The total annual cost for Flooring, excluding the cost of the wood itself but including the tools, machinery, labor and so on$,$ is $$737,100.$

The supervisor of the flooring department estimates the following time for each of the four processes for a unit of wood as sold:

Cutting: $11$ minutes

Planing: $18$ minutes

Distressing $($optional$)$: $24$ minutes

Staining $($optional$)$: $27$ minutes

During the year, Flooring received orders for $12,000$ units. Of these, $7,000$ units were distressed and $9,500$ units were stained.

Required:

a$.$ What is the cost per minute for activities in Flooring?

Note: Round your answer to $2$ decimal places.

b$.$ What is the cost of a unit that is cut, planed, and stained?

Note: Round your intermediate calculations and final answer to $2$ decimal places.

c$.$ How many minutes of unused capacity did Flooring have for the year?

d$.$ What was the cost of the unused capacity in Flooring?

Note: Round your intermediate calculations to $2$ decimal places and round your final answer to the nearest whole dollar.