Using the lagrangean multiplier approach calculate the

Question

You have determined that the service (Z) provided by BF is a function of its medical staff input (M) and social worker staff input (S) which is given by:

Z = 2M + S + MS - S²

BF's staff budget for the coming year is $600,000. Annual employment costs are $50,000 for each social worker staff member (S) and $100,000 for each medical staff member (M).

Using the Lagrangean multiplier approach calculate the optimal (i.e., service maximizing) combination of medical and social worker staff. Determine the optimal amount of service provided by BF.