The revenue department of a state government employs Chartered Accounts (CA) to audit corporate tax returns and Book Keepers(BK) to audit individual returns. CA's are paid $.31200 per year, while the annual salary of a bookkeeper is $18200.Given the current staff of CA s and bookkeepers, a study made by the department's economist shows that adding one year of a CA's time to auditing corporate returns results in an average additional tax collection of $ 52000. In contrast, an additional bookkeeper adds tax collections of $ 41600.
If the department's objective is to maximize tax revenue collected, is the present mix of CA s and bookkeepers optimal? Explain. If the present mix of CA s and bookkeepers is not optimal, explain, what reallocation should be made. That is, should the department hire more CA s and fewer bookkeepers or vice versa?