6. A business analytics company is considering five projects for the next month. The number of business analysts and the number of assistants required for each project, and the expected profit for each project are given below. Project 1 2 3 4 5 4 5 6 3 4 Business Analysts Required Assistants Required 3 4 5 4 5 Profit (in thousands of dollars) 200 300 240 180 250 The company wants to maximize the total profit subject to the following constraints: - Use no more than 22 business analysts - Use no more than 20 assistants - If project 1 is done, then project 2 must be done and vice versa - At least three projects must be selected (a) Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints. What type of integer optimization model is this? Briefly describe what the objective function and each constraint represent. (b) The optimal solution for the above problem is given below. Variable values are X1 = 1, X2 = 1, X3 = 1, X4 = 0, X5 = 1 Objective function value is 990 Interpret the optimal solution to make a recommendation to the company