Lipton Liquids produces three products by a joint production process. Raw materials are put into production in Department $1,$ and at the end of processing in this department, three products appear. Alpha is sold at the split$-$off point with no further processing. Beta and Gamma require further processing before they are sold. Beta is processed in Department $2,$ and Gamma is processed in Department $3.$ Lipton Liquids uses the estimated net realizable value method of allocating joint production costs.

No inventories were on hand at July $1,$ the beginning of the quarter. No raw material was on hand at September $30.$ All units on hand at September $30$ were fully complete as to processing. Following is a summary of costs and other data for the period ended September $30$:

Products Alpha Beta Gamma

Units sold $28,00082,60098,000$

Units on hand at September $3070,000056,000$

Sales revenues $ $126,000$ $ $743,400$ $ $1,029,000$

Departments $123$

Raw material cost $ $470,400$ $ $0$ $ $0$

Direct labor cost $201,600339,780805,350$

Manufacturing overhead $84,00088,620307,650$

Required:

Determine the following amounts for each product: $(1)$ estimated net realizable value used for allocating joint costs, $(2)$ joint costs allocated to each of the three products, $(3)$ cost of goods sold, and $(4)$ finished goods inventory costs, September $30.$

Assume that the entire output of Alpha could be processed further at an additional cost of $$12$ per unit and then sold for $$16\mathrm{.}30$ per unit. Compute the incremental income $($loss$)$ from further processing Alpha.

Considering the results of part b$,$ should Lipton Liquids process Alpha further?