3. Consider a decisional case of a Mutual Funds, Inc, located in Socorro (NM). The firm has just obtained $100,000 by converting industrial bonds to cash. Dr. Peter Anselmo, a chief financial executive, is now looking for other investment opportunities for funds. Peter has identified five investment opportunities and projected these annual rates of return. The investments and rates of returns are as follows: Investment Atlantic Oil Pacific Oil Midwest Steel Huber Steel Government Bond Projected Rate of Return 7.3 (%) 10.3 (%) 6.4 (%) 7.5 (%) 4.5 (%) The management has imposed the following investment guidelines: (a) Both oil and steel industries should not receive more than $50,000. (b) Government bond should be at least 25% of the steel industry investment. (c) The investment in Pacific Oil cannot be more than 60% of the total oil industry investment. (1) What portfolio recommendations should be made for the available $100,000? (2) Develop the dual formulation. Show optimal dual variables and discuss CSC from the dual