Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budged available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Also, if project 4 is selected, project 8 must also be selected. Also, if project 8 is selected, project 4 must also be selected. Following are the resource requirements and the estimated profit for each project:

The company wants to know which projects to select so that they maximize the profit. Formulate this problem.

(i) [5 Pt.] Define the decision variables.

(ii) [5 Pt.] Build the objective function as a MINIMIZATION problem.

(iii) [10 Pt.] Build all the constraints

Project Expense ($1,000s) 1 2 3 4 5 6 7 8 60 110 53 47 92 85 73 65 Management Scientist Required 7 9 8 4 7 6 8 5 Estimated Profit ($1,000,000s) 0.36 0.82 0.29 0.16 0.56 0.61 0.48 0.41