1. An investor has decided to invest at most $100,000 in securities in the form of corporate stocks. He has classified his options into three groups: blue-chip stocks that he assumes will yield a 10% return (dividends and capital appreciation) within a year, growth stocks that he assumes will yield a 15% return within a year, and speculative stocks that he assumes will yield a 20% return (mainly due to capital appreciation) within a year. Because of the relative risks involved in his investment, he has further decided that no more than 30% of his investment should be in growth and speculative stocks andat least 50% of his investment should be in blue-chip and speculative stocks. Determine how much should be invested in each group of stocks in the hope of maximizing the return on the investments.

a) Suppose the growth stocks are anticipated to yield a 12% return instead of 15%. Use a sensitivity analysis to determine whether this will cause a change in the optimal solution base.

b) Explain whether you recommend that the investor invest less than 50% of his investment in blue-chip and speculative stocks.

c) Explain whether you recommend that the investor invest more than 30% of his investment in growth and speculative stocks.

2. Submit a Word document and an Excel workbook showing how to solve the linear programming problem by using the Excel Solver, perform a sensitivity analysis, and apply duality to the original formulation.

The Excel workbook should contain the setup of the problem, the optimal solution obtained by using the Excel Solver, and the answer and sensitivity reports from Excel. Make sure to outline the formulation of the dual problem and verify the consistency of the dual solutions with those of the original problem.

In the Word document, include the standard form of the mathematical formulation of the problem, solutions obtained by the Excel Solver, and ensure that the scenario questions (a) through(c) are answered.

Furthermore, write the mathematical formulation of the dual problem, solve the dual problem, and explain whether the solutions obtained from the dual formulation are consistent with those of the original problem.