The state of Primavera is considering six large investments for water treatment. Each investment can be made only once, and fractions are not possible. These investments differ in the estimated number of people served as well as in the amount of capital required, as shown in the following table: Investment Opportunity 123456 Est. pop. served (millions) 15 12 16 18 9 11 Cost (millions) 38 33 39 45 23 27 Investment opportunities 1 and 2 are mutually exclusive and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunity 5 and 6. The objective is to select the combination of investments that maximizes the estimated number of people served, given that the total capital available for these investments is $100 million. Formulate a binary integer programming problem to determine which investments should be made. You do not need to solve the problem. You may define variables other than decision variables but ensure you clearly indicate which variables are decision variables