An investor has decided to invest at most $100,000 in securities in the form of corporate stocks. He hasclassified 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 least50% 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 theinvestments.

a) Describe the three components of the linear programming problem (the decision variables, objective function, and problem constraints), and the mathematical formulation of the problem in both standard and normal forms. Justify your reasoning for the formulation.