Bria Furniture sells bed frames and mattresses. One of its products is a premium therapeutic bed set produced by OmniSleep, which comes with a mattress and a bed frame. Bria offers a package consisting of the mattress, the frame, and on$-$site installation by its staff. All of these components can be sold separately, as often done by other vendors, so Bria concludes that these are separate performance obligations. Bria sells the OmniSleep package for $$5,100.$ The mattress and the frame are sold separately for $$3,050$ and $$1,905,$ respectively. Other vendors in the same area typically charge $$400$ for on$-$site installation. Bria does not sell on$-$site installation separately. On average, the prices charged by Bria are $10\%$ higher than those of its competitors. Bria estimates that it incurs about $$145$ of compensation and other costs to provide the installation service. The profit margin over cost is estimated to be approximately $40\%.$

Required:

$($a$)$ Estimate the stand$-$alone selling price of the installation service using the adjusted market assessment approach.

$($b$)$ Estimate the stand$-$alone selling price of the installation service using the expected cost plus margin approach.

$($c$)$ Estimate the stand$-$alone selling price of the installation service using the residual approach.