A rural clinic hires its staff from nearby cities and towns on a part-time basis. The clinic attempts to have a general practitioner (GP), a nurse, and an internist on duty during at least a portion of each week. The clinic has a weekly budget of $1,200. A GP charges the clinic $40 per hour, a nurse charges $20 per hour, and an internist charges $150 per hour. The clinic has established the following goals, in order of priority:
(1) A nurse should be available at least 30 hours per week.
(2) The weekly budget of $1,200 should not be exceeded.
(3) A GP or an internist should be available at least 20 hours per week.
(4) An internist should be available at least 6 hours per week.
a. Formulate a goal programming model to determine the number of hours to hire each staff member to satisfy the various goals.
b. Solve the model by using the computer.