Currently, the focus is on developing the following three sports amenities in the order outlined below: 1. Multi-purpose synthetic football field to FIFA and World Rugby accreditation standard 2. Multi-purpose courts for basketball, and futsal 3. 500m walking and running track For these amenities, there are four main jobs: 1. Excavation and field preparation 2. Construction of seated viewing grandstand and electronic scoreboard 3. Installation of sports and recreational lighting 4. Futureproofing for additional activities and amenities including food and beverage Not all amenities require all jobs to be performed. Due to the current COVID-19 restrictions, only one work crew is allowed to complete each job. Here are the details of the job sequence and processing times: Amenities Football Field Courts for basketball and futsal Walking and running track Job sequence 1,2,3 1,2,3,4 1,3,4 Job processing time (in weeks) t = 8, t = 8, t3 = 5 t = 4, t = 8,t3 = 4, t = 7 t = 9, t3 = 8,t4 = 5 Part(a) (10 points). Write the mathematical representation of this scheduling problem. Clearly identify the sets and parameters, decision variables, objective function, and constraints with their respective indices. Part(b) (5 points). What is the earliest project completion time and the slack of the jobs? Show all calculations and justify your answer. Part(c) (15 points). UNSW is now considering optimizing the job sequence of the three amenities in such a way that the entire project can be completed as soon as possible. i. Does the mathematical formulation presented in Part(a) need to change? If yes, write the new mathematical representation ii. Provide a feasible solution better than the solution obtained in Part (b) if any and justify your answer iii. Identify the non-linear constraints in the new mathematical representation if any. iv. Will this improve the earliest project completion time obtained in Part (b) If yes, justify your answer