Fundamentals of Cost Accounting 2nd Edition by William Lanen, Carolyn Wells, Michael Maher

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Effect of By-Product versus Joint Cost Accounting
Black Corporation processes xyrex into three outputs: Xy-1, Xy-2, and Xy-3. Xy-1 accounts for 60 percent of the net realizable value at the split-off point, Xy-2 accounts for 30 percent, and Xy-3 accounts for the balance. The joint costs total $182,750. If Xy-3 is accounted for as a by-product, its $18,800 net realizable value at split-off is credited to the joint manufacturing costs using method 1 described in the text, which credits the by-product's net realizable value as a reduction in the joint costs.
Required
a. What are the allocated joint costs for the three outputs
(1) If Xy-3 is accounted for as a joint product
(2) If Xy-3 is accounted for as a by-product
b. Management does not understand why joint costs are allocated to Xy-3 differently when it is accounted for as a by-product. Write a brief memo explaining why this occurs.