The Fleming Foundation is a charitable organization founded by Gaylord Fleming and Sandy Fleming. The Flemings intended for the charity to provide programs in health care for older persons, particularly those in poverty. The two main program divisions of the foundation are mental health and housing for elderly individuals. In addition to these programs, the foundation also provides health care educational programs and has a significant fund$-$raising effort to help the foundation grow and accomplish the goals of the founders. The foundation is organized into two operating departments$$education and program management. These departments are supported by two service departments$$information technology $($IT$)$ and administration. To summarize, there are four departments $($two service departments and two operating departments$)$ and two programs $($mental health and housing for older adults$).$ The service department costs are allocated to the operating departments, and then the operating department costs are allocated to the programs.

There are $$380,000$ of costs directly traceable to each of the four departments. An additional $$40,500$ of indirect costs is shared among the four departments$$$$25,500$ of which is allocated to the departments based on labor hours and $$15,000$ of which is allocated to the departments based The cost, labor hours, and head count in these departments in the most recent year are as follows:

IT serves education, administration, and program management $20\%,20\%,$ and $60\%$ of its time, respectively.

Administration serves education, IT$,$ and program management $60\%,10\%,$ and $30\%$ of its time, respectively.

The costs of the two operating departments $($education and program management$)$ are allocated to the two programs

$($mental health and housing$)$ as follows: the costs in Education are allocated on the basis of labor hours in the programs,

while the costs in program management are allocated using the head count used in the two programs. The following

table shows the labor hours and head count consumption by the two programs.Required:

Determine the costs allocated to the mental health and housing programs using the $($a$)$ direct method, $($b$)$ the step method $($assuming that IT goes first$),$ and $($c$)$ the reciprocal method. $($Do not round intermediate calculations. Round final answers to the nearest dollar.$)$