A consulting company has eight employees, each of whom can work on at most two team projects. Five projects are under consideration. Each project requires four of the eight employees. The required employees, the total revenue earned and the project fees that are payable to each employee for each project are shown in the following table: Required employees Project 1 3 4 1,2,3,4 5,6,7,8 1,3,5,7 2,4,6,8 1.2.7,8 Revenue R 200 000 R 400 000 R 600 000 R 500 000 R 600 000 Project fee R 20000 R 30000 R 40000 R 30000 R 50000 Each employee who works on any project must also be paid the fixed retainer shown in the table on the next page (irrespective of the number of projects to which an employee contributes). Employee 5 2 3 4 6 8 Retainer R5000 R7000 R8000 R4000 R9000 R 6000 R8000 R 5.000 Formulate an integer programming problem with which the consulting company can determine how to maximise its profit. You do not have to solve the model but define all parameters and variables in your model unambiguously. Furthermore, find the optimal solution(s) to this integer programming problem using an appropriate computer implementation (e.g., Microsoft Excel's Solver add-on or Python packages such as SciPy & PuLP). Interpret in words the solution obtained. Please include a carefully commented print-out of your program embedded within your PDF submission.