Nuts plc produces alpha and beta in two stages. The separation process produces crude alpha and beta
Question:
The refining process costs £125 per tonne for alpha and £50 per tonne for beta; no weight is lost in refining. The demand functions for refined alpha and refined beta are independent of each other, and the corresponding price equations are:
PA = 1250 - QA
PB = 666 2/3 - 100QB / 18
where
PA = price per tonne of refined alpha
PB = price per tonne of refined beta
QA = quantity of refined alpha
QB = quantity of refined beta
The company is considering whether any part of the production of crude alpha or crude beta should be treated as a by-product. The by-product would be taken away free of charge by a large-scale pig farming enterprise.
Requirements:
(a) If all the output of the separation process is refined and sold:
(i) Calculate the optimal quantity of raw material to be processed and the quantities and prices of the refined products; and
(ii) Determine the 'major' product which is worth refining and the 'minor' product which deserves consideration as a potential by-product, but do not attempt to calculate at this stage how much of the 'minor' product would be refined.
(b) Calculate:
(i) The optimal quantity of the 'major' product which would be worth producing regardless of the value of the 'minor' product; and
(ii) The quantity of the resulting 'minor' product that would be worth refining.
(c) Evaluate the principal methods and problems of joint-cost allocation for stock valuation, referring to Nuts plc where appropriate.
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