[Question 5] 4 The production manager of a Mining plant is attempting to devise a shift pattern for his workforce. Each day of every working week is divided into three eight-hour shift periods (00:01-08:00, 08:01- 16:00, 16:01-24:00) denoted by night, day and late respectively. The plant must be manned at all times and the minimum number of workers required for each of these shifts over any working week is as below: Mon Tues Wed Thur. Fri Sat Sun Night 5 3 2 3 2. 2 Day 7 8 9 5 7 2 5 Late 9 10 10 7 11 2 2 The union agreement governing acceptable shifts for workers is as follows: 1. Each worker is assigned to work either a night shift or a day shift or a late shift and once a worker has been assigned to a shift they must remain on the same shift every day that they work. 2. Each worker works four consecutive days during any seven day period. In total there are currently 60 workers. Formulate the production manager's problem as a linear program. Solve this problem as a linear program