A manufacturer's plant has two service departments (designated below as \(\mathrm{S}_{1}\) and \(\mathrm{S}_{2}\) ) and three production departments (designated below as \(\mathrm{P}_{1}, \mathrm{P}_{2}\) and \(\mathrm{P}_{3}\) ) and wishes to allocate all factory overhead to production departments. A primary distribution of overhead to all departments has already been made and is indicated below. The company makes the secondary distribution of overhead from service departments to production departments on a reciprocal basis, recognizing the fact that services of one service department are utilized by another. Data regarding costs and allocation percentages are as follows:

Matrix algebra is to be used in the secondary allocation process. The amount of overhead to be allocated to the service departments you express in two simultaneous equation as:

{Required:}
(1) The system of simultaneous equations above may be stated in matrix form as

(2) For the correct matrix \(A\) in item (I), there exists a unique inverse matrix \(A^{-1}\). Multiplication of the matrix \(\mathrm{A}^{-1}\) by the matrix A will produce

a. The matrix A'

b. Another inverse matrix.

c. The correct solution to the system.

d. An identity matrix.
(3) Without prejudice to your previous answers, assume that the correct matrix form in item (1) was:

(4) The total amount of overhead allocated to department \(S\), after receiving the allocation from department \(\mathrm{S}_{2}\) is

a. \(\$ 141,779\).

b. \(\$ 124,000\).

c. \(\$ 121,520\).

d. \(\$ 117,600\).
(5) The total amount of overhead allocated to department \(\sim 2\) after receiving the allocation from department \(S_{1}\) is

a. \(\$ 392,000\).

b. \(\$ 220,000\).

c. \(\$ 130,000\).

d. \(\$ 127,400\).
(6) Without prejudice to your previous answers, assume that the answer to item (4) is \(\$ 100,000\) and to item (5) is \(\$ 150,000\); then the total amount of overhead allocated to production department \(P\), would be

a. \(\$ 1,508,104\).

b. \(\$ 1,495,000\).

c. \(\$ 1,489,800\).

d. \(\$ 108,104\).

Transcribed Image Text:

Service Department Overhead Cost Allocation Percentages to be Allocated to Departments Service Department S $2 P1 P2 P3 S 0% 10% 20% 40% 30% S 20% 0 50% 10% 20% Primary Overhead to be Allocated $98,000 $117,600 $1,400,000 $2,100,000 $640,000