excel problem. Formulate an algebraic binary integer programming model and solve it on a spreadsheet for this problem

4. The board of directors is considering six large capital investment options. Each investment option carn be made only once. These options differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table Estimated Profit (Smillions 10 15 19 apital Required (Smillions) 25 30 50 15 40 30 Investment option 4 17 13 The total amount of capital available for these investment options is $90 million. Investment options 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two options is undertaken. There are no such restrictions on investment options 5 and 6.The objective is to select the combination of the options that will maximize the total estimated long run profit (net present value) (a) Formulate an algebraic binary integer programming model and solve it on a spreadsheet for this problem (b) Perform sensitivity analysis on the amount of capital made available for the investment options (in millions): 70, 80, 90, 100, 110 and 120. Include both the optimal values of the decision variables and objective function in the output. Interpret your analysis results