A restaurant is open 24 hours a day. Servers work in one of 4 possible 12-hour shifts as follows Shift #1: 3 A.M.-3 P.M. Shift #2: 9 A.M.-9 P.M. Shift #3: 3 P.M.-3 A.M. Shift #4: 9 P.M.-9 A.M. The following table shows the minimum number of workers needed during the 4 periods into which the day is divided: Period Time Number of servers required 1 3 A.M.- 9 A.M. 12 2 9 A.M.- 3 P.M. 10 3 3 P.M.-9 P.M. 9 4 9 P.M.- 3 A.M. Moreover, based on the past experience, the manager wants to control the number of servers who work in Shift #1 no more than 6, since she cannot find that many servers who are willing to so based on past experience. The question is to determine how many servers should report for work in each shift, so that the total number of servers required for one day's operations is minimized. a. Please clearly define decision variables and write down the objective function of this problem including whether to minimize or maximize. b. Please write down all constraints for this problem c. In the optimal solution, what is the number of servers who work in Shift #4