he taxpayer Assistance Center (TAC) is a division of the IRS which provides free assistance to individuals to help them in the preparations of their tax returns.
The number of individuals that receive assistance (q), is a function of the number of professional accountants (A) and trained tax preparers (T) employed in a given office.
The function relating the number of persons assisted in an office (q) is related to the employment levels of accountants (A) and preparers (T) as follows:
Q=250A+100T+25AT
Assume a TAC office has an annual employment budget of $350,000 to spend on accountants and tax preparers and the annual salary of an accountant is $50,000 and the annual salary of a tax preparer is $25,000.
A. A. Using the Lagrangian technique, what is the optimal combination of accountants (A) and tax preparers (T), per office, if the objective or goal of the office is to maximize the number of individuals assisted (q).
B. B. Under the annual budget of $350,000 what is the maximum number of individuals that can be assisted by a TAC office?
C. At the optimal use of accountants and tax preparers, how many (decimal fractions OK) individuals can be assisted by a $1 increase in the budget? How did you determine this?
