A factory has two production departments (P1 and P2) and two service departments (X and Y). Overheads allocated and apportioned so far are X $20,000 and Y $12,000. The service departments' work is used as follows: X: P1 40%, P2 40%, Y 20% Y: P1 50%, P2 30%, X 20% Using the reciprocal (algebraic) method, what is the total service department overhead charged to P1, to the nearest $?

Correct answer: C) $17,667

Explanation

Let X and Y be the total overheads of each service department after reciprocal charges. X = 20,000 + 0.2Y and Y = 12,000 + 0.2X. Substituting: X = 20,000 + 0.2(12,000 + 0.2X) = 22,400 + 0.04X, so 0.96X = 22,400 and X = 23,333.33. Y = 12,000 + 0.2 x 23,333.33 = 16,666.67. Charge to P1 = 0.4 x 23,333.33 + 0.5 x 16,666.67 = 9,333.33 + 8,333.33 = $17,666.67, which is $17,667 to the nearest $.