Northwest Building Products $($NBP$)$ manufactures two lumber products from a joint milling process: residential building lumber $($RBL$)$ and commercial building lumber $($CBL$).$ A standard production run incurs joint costs of $$540,000$ and results in $96,000$ units of RBL and $144,000$ units of CBL$.$ Each RBL sells for $$10$ per unit and each CBL sells for $$12$ per unit.

Required:

$1.$ Assuming that no further processing occurs after the split$-$off point, how much of the joint costs are allocated to commercial lumber $($CBL$)$ on a physical measure method basis?

$2.$ If no further processing occurs after the split$-$off point, how much of the joint cost is allocated to the residential lumber $($RBL$)$ using a sales value at split$-$off method?

$3.$ Assume that the CBL is not marketable at split$-$off but must be planed and sized at a cost of $$360,000$ per production run. During this process, $12,000$ units are unavoidably lost and have no value. The remaining units of CBL are salable at $$14$ per unit. The RBL$,$ although salable immediately at the split$-$off point, is coated with a tarlike preservative that costs $$240,000$ per production run. The RBL is then sold for $$12$ each. Using the net realizable value basis, how much of the completion costs should be assigned to each unit of CBL$?$ Should NBP choose to process RBL beyond split$-$off?