Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs.

The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number.)

sales department
service department

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-10-15T04:43:59+02:00

Answer:

The total cost of sales department is [tex]a = \$ 84,000[/tex]

The total cost of services department is [tex]b = \$ 21,000[/tex]

Step-by-step explanation:

From the question we are told that

The direct for sales cost is [tex]SC = \$88,200[/tex]

The direct cost for service department is [tex] SV = \$29,400[/tex]

Given that the sales department charges 10% of its total monthly costs to the service department

The indirect cost of service department is 10% of a = 0.10 a

Here a is the total cost of sales

Given that the service department charges 20% of its total monthly costs to the sales department

The indirect cost of sales department is 20% of b = 0.20 b

Here b is the total cost for service department

Generally the direct cost of sales can be mathematically represented as

[tex]SC = a + 0.20b [/tex]

=> [tex]88200 = a + 0.20b[/tex]

=> [tex]a = 88200-0.20b[/tex]

Generally the direct cost of services can be mathematically represented as

[tex]SV = b + 0.10a [/tex]

=> [tex]29400 = b + 0.10a[/tex]

substituting for a in the above equation

=> [tex]29400 = b + 0.10 [88200-0.20b][/tex]

=> [tex]b = \$ 21,000[/tex]

substituting this value into the equation for a

[tex]a = 88200-0.20 (21000)[/tex]

=> [tex]a = \$ 84000[/tex]