MGT 397 CHAPTER 5 ASSIGNMENT 1. City Research Inc. is contemplating a research and development (R&D) program encompassing five potential research projects named 1, 2, 3, 4, and 5. All the projects are expected to go on simultaneously. The company is constrained from embarking on all projects by the number of scientists it has and the budget available for R&D projects. The company has 22 scientists and $250,000 (two hundred and fifty thousand dollars) budgeted for R&D program. Since projects 2 and 5 require the involvement of the same scientists, both of them would not be selected, but either may or may not be selected. Furthermore, if project 3 is selected, project 5 must also be selected and vice versa. The Table below shows the expense for cach project, the number of scientists required, and the estimated profit in millions of dollars associated with each project. Projec Expense (S) Scientists Required 18 11 55.000 80,000 44,000 50.000 80.000 Estimated Profit (SMillions) (51,000,000) 30 .20 .5 .6 5 7 2 1 3 6 7 S 5 Formulate the integer programming (IP) model for this problem that will maximize profit. That is; (i) Define the decision variables. (ii) State the objective function. (iii) State all the constraints. I am asking for the IP formulation only. (Hint: This is a 0-1 integer programming problem. Refer to, and study examples and information in the textbook (pages 187 & 188), and on Blackboard)