Your corporation has just approved an 8-year expansion plan to grow its market share. The plan requires an influx of cash in each of the 8 years. Management wants to develop a financial plan to ensure the cash needed for the expansion will be available at the beginning of each of the 8 years. The corporation has the following investment options: Security Price per unit Return Rate (%) Years to Maturity 1 $1,200 10.255 5 2 $1,000 6.7550 6 3 $1,175 12.110 7 Savings Account 5.500 Each unit of security 1, 2, and 3 guarantees to pay $1,000 at maturity. Investments in these securities must take place only at the beginning of year 1 and will be held until maturity. Any funds not invested in securities will be invested in a savings account that pays the annual interest rates noted above. The following table summarizes the cash needs for the expansion plan for each of the 8 years: Year 1 = $250,000 Year 5 = $295,000 Year 2 = $300,000 Year 6 = $310,000 Year 3 = $225,000 Year 7 = $280,000 Year 4 = $235,000 Year 8 = $305,000 a. Develop a linear programming model to minimize the total dollars needed to be invested now to meet the expansion cash needs in the next 8 years. Hint: this is the objective function. Use Excel Solver, solving method: Simplex LP. b. How many units of each security 1, 2, and 3 should the corporation purchase? What is the investment amount in each security 1, 2, and 3 in year 1? c. How much should the corporation place in the savings account in each of the 8 years? d. Assuming the corporation currently has $1.8 Million available cash to invest and given the cash needs for the expansion, is the investment plan that you developed feasible? Explain your answer and provide reasoning.