QUESTION 4: Linear Programming Formulation (20 points) Niteten Power and Light Company (NPLC) wants to develop an efficient work schedule for its full- and part-time customer service clerks. The number of clerks needed to provide adequate service during each hour the office is open on a weekday is given below: Hour 8-9AM 9-10 10-11 11-12PM 12-1 1-2 2-3 3-4 Clerks 5 4 6 8 10 9 7 4 A full time clerk works 3 hours, has a 1-hour break, and then works another 3 hours. Part-time clerks work for 4 consecutive hours. Full-timers get paid for their break. All clerks start work on the hour. NPLC's office manager insists that at least one full time clerk be on duty during all open hours and that at least 40% of the clerks should be full-time clerks on payroll. A full-time clerk costs NPLC $20 per hour, and a part-timer costs $15 per hour. Formulate a linear programming model that will provide a schedule that will meet NPLC's customer service needs at a minimum labor cost. (Define the decision variables, objective function, and constraints). DO NOT SOLVE. Hint on the decision variables: there are 2 different full-time shifts and 5 different part-time shifts