1.(Buildup graphs.) Consider a continuous operation in which raw tomatoes arrive to a processing unit in bulk. The tomatoes arrive at an average steady rate of 75 tons per hour from 8 a.m. to 1 p.m. every day. The processing begins as soon as the tomatoes start arriving, at 8 a.m. However, the processing unit can only process at a steady rate of 25 tons/hr. If need be, the processing unit can process for 24 hours a day. If tomatoes arrive when the processing unit is busy, a queue of inventory will form.a.[1 point] How many hours a day does the processing unit operate?b.[1] What is the maximum inventory of raw tomatoes?c.[1] What is the capacity utilization of the processing unit?(Hint: This is equivalent to the fraction of a day the plant operates)d.[2] How long on average does a tomato stay in the queue?(Hint: First calculate average inventory (\(=\) AREA/T) and average throughput for the entire time the processing unit is operating. Then use little's law to calculate CT.)2. A specialty pain clinic treats patients with severe joint pain using their proprietary Myofascial Therapy that combines deep pressure massage with physical therapy. To begin with, a patient undergoes first round of treatment that lasts one month. At the end of the first round, the patient is evaluated. Based on historic data, there is a \(70\%\) probability that the treatment is successful, in which case the patient is discharged. If not, the patient commences a second round of more aggressive treatment, which lasts another month. It is estimated that among patients who go through first two rounds of treatment, \(50\%\) do not return for a third round (because of a successful treatment, financial limitations, personal reasons, etc.) Of those who do return, they undergo the third and final round of treatment that lasts, on average, 2 months.On average, ten new patients arrive at the clinic every business day. Assume 20 business days per month.a.[3] What fraction of the clinic's patients are in their second round of treatment? (Hint: Use Little's law for each round of treatment to calculate INV)b.[2] Patients pay \(\$ 500\) per month of treatment. What are the annual revenues of the clinic?(Note: It may be helpful to draw a process flow diagram.)