HITEC 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 25 scientists and $220,000 (two hundred and twenty 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, but not vice versa. The Table below shows the expense for each project, the number of scientists required, and the estimated profit in millions of dollars associated with each project.

Project	Expense ($)	Scientists Required	Estimated Profit ($Millions, $1,000,000)
1	50,000	8	3.0
2	70,000	6	6.0
3	45,000	3	3.5
4	49,000	4	1.5
5	80,000	9	5.5

Formulate the integer programming (IP) model for this problem that will maximize profit for HITEC Inc.That is;

(i) Define/state the decision variables.

(ii) State the objective function.

(iii) State all the constraints.

Use IP formulation only. Do not solve with the software.