In MA, child support is generally one of the more straightforward areas. There is a guideline or formula that would be used and the Court is supposed to make a written finding if the guidelines are not being used within 2 percentage point. The typical formula first looks at what the income for the recipient spouse( Marge) and what the cost of child care, health and dental and prior support orders is to her. The guidelines examine how many children ( 3) Bart, Lisa and Maggie. The guidelines then look at the GROSS income of the payer spouse, Homer and his cost for health, dental, child care costs minus any other support obligations. So for example, if Marge is a stay at home Wife with no income or obligations and Homer made $1000 gross a week and pays $100 a week for Health and Dental then under the guidelines, Homer would pay Marge $284.
There are reasons why the guidelines are not followed or are harder to determine Figuring out income for those without w-2 earning, self employed individuals, overtime, bonuses, second jobs, different child sharing and so forth. Looking at the Simpson's it appears to be that Homer has a pretty straightforward job but that both he and Marge have entrepreneurial spirit and how to figure out all of there additional income.
Generally, it would be up to Marge to choose if the money will be paid to DOR by Homer's attached check. Other issues include who would claim the dependency exemptions for tax purposes. Homer likely would becuase unless Marge makes a certain amount of money ( over $20,000) there is no benefit to her. If she is making more money child support can be modified and parties can each claim one child and alternate one child. There are questions when a child is emancipated along with college expenses( less likely for Bart) and extracurricular activities not directly related but to be examined.