Question: Bright Future, Ltd (BF) is a nonprofit foundation providing medical treatment to emotionally distressed children. BF has hired you as a business consultant to design an employment policy that would be consistent with its goal of providing the maximum possible service given its limited financial resources. You have determined that the service (Z) provided by BF is a function of its medical staff input (M) and sound service input (S) which is given by:

BF’s staff budget for the coming year is $1,200,000. Annual employment costs are $30,000 for each social service staff member (S) and $60,000 for each medical staff member (M).

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

(b) Calculate BF’s marginal cost.

(c) Using Excel-Solver verify your answer to (a).