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 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