Linear programming problem. Please include all the steps.

1 (5 points). Continue on the small town walk-in clinic example. The two doctors, Phil and Dave, concluded that to better serve their patients, they needed another clinic partner. A third doctor, Mary, joined in. By analyzing the new data with three doctors working in the clinic, they found that the probability distribution for the number of patients in the clinic at a given time is as follows P = {0.11, 0.23, 0.23, 0.15, 0.10, 0.07, 0.05, 0.03, 0.02, 0.01}. It remained the same that on average 8 patient per hour arrive and stay see the doctors. (a) Find the average number of patients in the clinic at a given time. (b) Find the average number of patients in the waiting room at. a given time. (c) Find the expected number of patients being treated at a given time. (d) Find the average time a patient is in the clinic. (e) Find the average time a patient is in the queue. (f) Find the average time a patient is visited by a doctor. (g) Find the utilization factor for the clinic