Consider a fictional manufacturing company, GreenTech Industries, which produces a range of eco$-$friendly home appliances. The company has three production departments $-$ Assembly, Finishing, and Packaging $-$ and two service departments $-$ Maintenance and Human Resources $($HR$).$

The annual costs for each department are as follows:

$-$ Maintenance: $$500,000$

$-$ Human Resources: $$300,000$

$-$ Assembly: $$1,000,000$

$-$ Finishing: $$700,000$

$-$ Packaging: $$400,000$

The service departments provide services to each other and to the production departments.

The percentage distribution of services provided by each service department is given below:

$-$ Maintenance: $20\%$ to HR$,30\%$ to Assembly, $25\%$ to Finishing, and $25\%$ to Packaging.

$-$ HR: $10\%$ to Maintenance, $40\%$ to Assembly, $30\%$ to Finishing, and $20\%$ to Packaging.

Required:

As a management accountant for GreenTech Industries, your task is to allocate the costs of the Maintenance and HR departments to the production departments using both the direct method and the step$-$down method. Ensure to provide detailed calculations for each method and discuss the advantages and limitations of each method in the context of GreenTech Industries. Additionally, comment on how the choice of allocation method might impact decision$-$making within the company.