Problem $3(29$ points$)$: Investment decisions

Maureen Laird is the chief financial officer for the Alva Electric Co$.,$ a major public utility in the

Midwest. 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 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 minimum cash flow

requirements in those years, as shown in the following table.

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 algebraically a Linear Programming model for this problem $(12$ points$).$

b$.$ Use the algebraic formulation in part $($a$)$ to check$/$proof the possibility of purchasing

$100$ units of asset $1,100$ units of asset $2,$ and $200$ units of asset $3.$ How much cash flow

would this mix of investments generate $5,10,$ and $20$ years from now? What would be

the total amount invested? $(4$ points$)$

c$.$ Formulate this same linear programming problem on a spreadsheet and SOLVE using

Excel Solver $($Provide the corresponding "Excel Spreadsheet" and the "Answer

Report"$).$ Include "managerial statements" that communicate the results of the

analyses. $($i$.$e$.,$ describe verbally$/$narratively the results. Don't forget to include how

much cash flow the optimal mix of investments would generate $5,10$ and $20$ years from

now$).(13$ points$)$