a QUESTION 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 Cosmetic Dermatology Orthopedic Neurosurgery Total hours available per week with present staff and facilities Lab 5 5 2 4 200 Hours required by patient X-ray Therapy Surgery 2 1 4 8 10 8 1 0 16 5 8 10 140 110 240 Physicians 10 14 8 12 300 The physicians have access to as many of each type of patient as they wish. Additionally, they have limited their cosmetic and dermatology practice to a combined total of no more than 125 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)