A company is considering the seven independent investment projects listed below. Each project has an initial investment required, the payoff as a net present value and the time required on the project by an expert consultant (in months). The company has a total budget of R450 000 and 12 months of expert consultant time available for all projects. Each project can either be accepted in total or be rejected in total. Project Initial investment Net present value Expert consultant time Project A R110 000 R100 000 2 Project B R70 000 R90 000 1 Project C R60 000 R60 000 3 Project D R95 000 R60 000 1 Project E R50 000 Project F R70 000 R90 000 Project G R78 000 R100 000 R65 000 2 1 4 a. Formulate the problem as a mathematical programming model by specifying the decision variables, the objective function, the constraints and restriction on decision variables. b. Use the Solver tool in a spreadsheet to find an optimal solution to this capital rationing investment decision. Provide as your answer the selected projects, the total NPV, total budget and total time required by the consultant.