The Wellness Center is an organization providing help to distressed students on campus during the two weeks exam period at the end of every semester. You've been hired as a business consultant to help the Center develop a hiring policy so that it can provide the most meaningful student service (S) possible. You've determined that service can be described as a function of Medical (M) and Counseling (C) staff input as follows: S = M + 0.5C + 0.5MC - C2
The staff budget for the Wellness Center for the coming semester is $1,200.00. Each member of the medical staff costs $60 and each member of the counseling staff costs $30.

(a) Determine the optimal combination of medical and counseling staff for the Wellness Center.

(b) Solve for and interpret the Lagrangian multiplier.

(c) If the Center were required to break even, what fee per service would you recommend that they charge?