Dakota Security Systems $($DSS$)$ is a decentralized organization that evaluates divisional management based on measures of divisional contribution margin. Residential Division and Commercial Division both sell security and monitoring equipment. Residential sells primarily to home owners and apartment management companies. Commercial focuses on small to medium$-$sized businesses. Residential sells a particular alarm to the outside market for $$267$ per unit. The outside market can absorb up to $49,700$ units per year. These units require $3$ direct labor$-$hours each.

If Residential modifies the units with an additional $0\mathrm{.}75$ hour of labor time, it can sell them to Commercial for $$294$ per unit. Commercial will accept up to $42,600$ of these units per year.

If Commercial does not obtain $42,600$ units from Residential, it purchases them for $$303$ each from the outside. Commercial incurs $$159$ of additional labor and other out$-$of$-$pocket costs to convert the alarm $($either from Residential or outside$)$ into one that fits in an existing Commercial Division system. The units can be sold to the outside market for $$663$ each.

Residential estimates that its total costs are $$1,502,000$ for fixed costs, $$54\mathrm{.}00$ per direct labor$-$hour, and $$21\mathrm{.}60$ per alarm for materials and other variable costs besides direct labor. Its capacity is limited to $238,500$ direct labor$-$hours per year.

Required:

Determine the following:

a$.$ Total contribution margin to Residential if it sells $49,700$ units outside.

b$.$ Total contribution margin to Residential if it sells $42,600$ units to Commercial.

c$.$ and d$.$ The costs to be considered in determining the optimal company policy for sales by Residential.

The annual contributions and costs for Residential and Commercial under the optimal policy.