Maureen Laird is the chief financial officer for the Alva Electric Co., a major public utility in the mid-west. The company has scheduled the construction of new hydroelectric plants 5, 10, and 20 years from now to meet the needs of the growing population in the region served by the company. To cover at least the construction costs, Maureen needs to invest some of the company's money now to meet these future cash-flow needs. Maureen may purchase only three kinds of financial assets, each of which costs $1 million per unit. Fractional units may be purchased. The assets produce income 5, 10, and 20 years from now, and that income is needed to cover at least minimum cash-flow requirements in those years. (Any excess income above the minimum requirement for each time period will be used to increase dividend payments to shareholders rather than saving it to help meet the minimum cash-flow requirement in the next time period.) The following table shows both the amount of income generated by each unit of each asset and the minimum amount of income needed for each of the future time periods when a new hydroelectric plant will be constructed. Income per Unit of Asset (Million Dollars) Asset 1 Asset 2 Asset 3 (Million Dollars) Year 5 2.0 1.0 0.5 10 0.5 0.5 1.0 20 0.0 1.5 2.0 Minimum Cash Flow Required 400 100 300 Maureen wishes to determine the mix of investments in these assets that will cover the cash-flow requirements while minimizing the total amount invested. (a) Formulate a linear programming model for this problem. (b) Solve this model by TORA, Excel Solver or other software. What is the resulting total amount invested (in million dollars). Show the printouts. (c) Determine the three relevant equations for this optimal solution.