(a) A company has two operating departments A and B, which respectively produce pens and pencils, and one service department which supplies the required power for the whole company. Some of the parts produced by Bare required by A to be incorporated in the pen. The matrix 0 1 below shows the amount of each department's product required by the other.

Departmental provisions

(A) Pen (units)

(B) Pencil (units)

Power (KW)

Departmental requirements

(per unit)

Pen Pencil Power 0 0 0 0.3 0 0 2.7 6.3 0.1 The three departments require three external resources- plastic, labour and oil- and the matrix D below gives the details for one gross unit of final product.

Departmental requirements per unit of finished product External resource Pen Pencil Power Plastic (g) 2.0 1.0 0 Labour (hr) 0.3 0.1 0.5 Oil (I) 0 0 0.5 The required number of pens and pencils for sale for the month are respectively 200k and 1 OOk.

REQUIRED

(i) Gross output for the month for each department

(ii) Total quantity of external resources needed for this level of output All calculations to the nearest k.

(b) The allocation of service costs to production departments has always been a problem for accountants. Two methods applying matrix algebra have been suggested as solutions.

REQUIRED Briefly describe these methods, and how they differ from each other.

Which method is preferable, and why?

University of Birmingham, Degree of BCom(Accounting), Accounting G, June 1977.