Remember the mathematical programming model for the optimal clinical appointment scheduling problem that we formulated in the class. Please see Lecture 04, pages 25-27 forthe parameters, variables, and model formulation for the problem.a)(15pts) Suppose that the clinic manager decides that the first patients must arrive inthe clinic at the same time [i.e. their appointment time is equal to the clinic opening time (= 0)]. Formulate a linear constraint for this restriction to add it into the current formulation. b)(10pts) The clinic managers, in general cases, make the decision of calling two patients at the sametime at the beginning of a day, because they may be highly sensitive about the minimization of one of the performance measures. Which performance measure is that in particular? c)(10pts) In the original formulation above, some assumptions were made about the arrivals of patients to the clinic to simplify the actual appointment scheduling problem. Write down one of thoseassumptions.