[Mathematical Programming Formulation] A professor requires students to form groups to do a class project. and formed a project group. Now, they want to divide the project work between them. The time to complete a task is different for Ali and Aye. Project tasks, task durations for each person, and some requirements are given below. We would like to formulate an appropriate integer program so that the students spend the least amount of time to complete all tasks. Hours needed Task 1 Task 2 Task 3 Task 4 9 2 4 3 7 5 6 5 Each person has to do exactly two tasks. If Ali does task 1, then he cannot do task 4. If Aye does task 3, then Ali has to do task 2. 1. Ali 2. Aye (a) (2 points] Define the decision variables with all necessary information. (b) [3 points) Write the objective and objective function mathematically. (c) [7 points) Write the constraints mathematically