Suppose the development department of a firm charges 10% of its total monthly costs to the promotional department, and the promotional department charges 5% of its total monthly costs to the development department. The direct costs of the development department are $25,400, and the direct costs of the promotional department are $9,400. The solution to the matrix equation or the column matrix gives the total costs for each department. Note that this equation can be written in the form or , which is the form for an open economy. Find the total costs for each department in this (micro)economy.
A) development = 27,000, promotional = 11,000
B) development = 27,000, promotional = 12,000
C) development = 26,000, promotional = 12,000
D) development = 38,000, promotional = 12,000
E) development = 26,000, promotional = 11,000

Question

Suppose the development department of a firm charges 10% of its total monthly costs to the promotional department, and the promotional department charges 5% of its total monthly costs to the development department. The direct costs of the development department are $25,400, and the direct costs of the promotional department are $9,400. The solution to the matrix equation  or the column matrix  gives the total costs for each department. Note that this equation can be written in the form  or  , which is the form for an open economy. Find the total costs for each department in this (micro)economy. ​
A) development = 27,000, promotional = 11,000 
B) development = 27,000, promotional = 12,000 
C) development = 26,000, promotional = 12,000 
D) development = 38,000, promotional = 12,000 
E) development = 26,000, promotional = 11,000

Quizplus · Accepted Answer

Let D be the total costs of the development department and P be the total costs of the promotional department. Then we have the following system of equations:

D = 25,400 + 0.1P
P = 9,400 + 0.05D

Substituting the first equation into the second, we get:

P = 9,400 + 0.05(25,400 + 0.1P)
P = 9,400 + 1,270 + 0.005P
0.995P = 10,670
P = 10,700

Substituting this value of P into the first equation, we get:

D = 25,400 + 0.1(10,700)
D = 26,470

Therefore, the total costs for the development department is $26,470 and the total costs for the promotional department is $10,700. The closest choice is C: development = 26,000, promotional = 12,000.

Suppose the Development Department of a Firm Charges 10% of Its