Dr. Malcomb Heizer wishes to invest his retirement fund of $2,000,000 so that hi

Question

Dr. Malcomb Heizer wishes to invest his retirement fund of $2,000,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low. He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 4 percent; stocks that have an expected return of 14 percent; and a money market mutual fund that is expected to return 18 percent. He has decided that the total $2,000,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, he may have some money invested in all three alternatives. He has also decided to invest, at most, 30 percent of this in stocks and at least 20 percent of this in money market funds. Formulate this as a linear programming problem and carefully define all the decision variables.Formulate this problem.

Explanation / Answer

Let a,b and c be the investments made in CDs, Stocks and Money market mutual funds respectively The objective function is to Maximize returns Max Z = 0.4 a + 0.14 b + 0.18 c Subject to a + b + c $2,000,000 (Total Amount Constraint) b $600,000 (Maximum Investment in Stock constraint) [Maximum 30% = $2m * 30% = $600,000] a + c $400,000 (Money Market constraint) [Minimum 20% = 20% * $2m = $400,000] a,b,c 0 (Non Negativity Constraint)

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