1) Botswana Electronics Company (BEC), is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all of the projects by the number of available scientists (40) and the budget available for the projects ($300,000). In the following are the resource requirements and the estimated profit for each project. Project Expense (S000) Scientists Required Profit ($000) 1 65 5 41 2 73 8 48 3 85 6 61 4 92 7 56 5 47 4 16 6 53 8 29 7 110 9 82 8 60 7 36 a. Using binary variables write down an algebraic formulation of an integer {linear} programming formulation for this problem. Document your algebraic model so that it is clear what the variables, constraints, and objective function mean. b. Implement your model in Solver. Document your model appropriately so it is possible to identify the decision variables, objective function, and constraints without going into Solver. Make sure to paste the Solver dialog box into your spreadsheet. c. Based on the solution to your model, what is the maximum profit? Which projects should be selected to achieve this profit? d. Suppose projects 3 and 7 are mutually exclusive. That is, BEC should not undertake both. Write down a linear constraint that implements this condition. e. Add the constraint from part d into your model and reoptimize your model. Do this in a separate worksheet. (You can right click the name of the original sheet of your model and select move or copy. Then make a copy of your original sheet, rename it and then make changes to the solver model therein). f. What is the revised project portfolio and the revised maximum profit? g. In addition to the previous restrictions, suppose that projects 1-4 involve consumer products and that management decides to undertake at least two of those. Write down a single linear constraint that implements this restriction. h. Add the constraint from part g into your model from part e and reoptimize your model. Do this in a separate worksheet. i. What is the revised project portfolio and revised profit