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 ($000) 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 1 10 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