Carlos is a fund manager from investment bank department of Star-Village. He is planning for next year's capital budget. There are 6 different projects available for investment. The net present value (NPV) and initial cost required for each project are listed as follows ( $ millions): The total budget for all projects is $250 million. There are certain conditions of restricting the investment alternatives: - Project 1 cannot be taken unless both project 3 and 4 are also undertaken. - If Project 2 is taken, then Project 5 cannot be taken. - If either Project 1 or Project 5 is taken, they must both be taken. - At least two projects from Project 1, 2, 3 and 4 must be taken. Formulate a binary integer program that will help Carlos to maximize his final expected return, while satisfying all the given restrictions. (35 marks)