A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse. Each of these requires different funding over the next two years and the net present value of the investments also varies. The following table provides the required investment amounts (in $1,000s) and the net present value (NPV) of each (also in $1,000s) INVESTMENT NPV YEAR 1 YEAR 2 Apartment 18 40 30 Shopping Center 15 30 20 Mini Warehouse 20 20 14 The company has $80,000 to invest in year 1 and $50,000 to invest in year 2. (a) Develop an integer programming model to maximize NPV in this situation (2 marks) (b) Suppose that the shopping center and the apartment would be on adjacent properties, and the shopping center would only be considered if the apartment were also built, formulate the constraint that would stipulate this. (2 marks) (0) Formulate a constraint that would force exactly two of the three projects to be undertaken (2 marks)