2 (35 points: Variables-5 points; Objective function-9 points; constraints-20 points; part b) 10 points) Carolina Health Services, Inc., is a clinic specializing in four types of patient care: cosmetic surgery, dermatology, orthopedic surgery, and neurosurgery. It has been determined from past records that a patient in each of these specialties contributes to the profit of the clinic as follows: cosmetic, $200; dermatology, $150-; orthopedic, $150; and neurology, $250. The physicians are convinced that patients are not being processed in an optimal manner. The clinic has contracted with you to provide a weekly patient processing system. You have been able to determine the following time requirements and limitations: Specialty Hours required by patient Therapy Surgery Physicians 10 Lab X-ray Cosmetic 5 2 1 4 Dermatology 5 8 10 8 14 Orthopedic 2 1 0 16 8 Neurosurgery 4 5 8 10 12 Total hours available per week 200 140 110 240 320 with present staff and facilities The physicians have access to as many of each type of patient as they wish. Additionally, they have limited their cosmetic and orthopedic practice to a combined total of no more than 120 hours a week. a) Define your decision variables and set up objective function and constraints to find the optimal patient mix on a weekly basis (set up your LP)