The Taxpayer Assistance Center (TAC) provides taxpayer assistance to help in the preparation of individual tax returns. The amount of assistance (A) that can be provided is a function of the number of professional accountants (P) and trained tax preparers (T) that are employed. The function is given by:

A = 500P +200T +50PT

(a) TAC has budgeted $700,000 for a new office to pay for the accountants and the tax preparers. It pays an accountant $100,000 and a tax preparer $50,000. Using the Lagrangean multiplier approach calculate the optimal staff combination that can maximize the amount of tax assistance. Determine the optimal amount of assistance provided by TAC. Explain your calculations.

(b) Calculate the marginal cost of providing additional assistance. Explain your answer.

(c) Using Excel-Solver verify your answer to (a). (Note: Provide the screenshots of the spreadsheet along with Solver windows as shown in the Solver supplement so that all Solver commands can be seen.)