A winner of the Texas Lotto has decided to invest $50,000 per year in the stock

Question

A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock.
The following table provides a summary of the return and risk:
STOCK               RETURN        RISK

Petrochemical     12%              9
Utility                  6%               4
The investor would like to maximize the return on the investment, but the average risk index of the in-vestment should not be higher than 6. How much should be invested in each stock? What is the average risk for this investment? What is the estimated return for this investment?

Explanation / Answer

Let X1= the number of dollars invested in petrochemical stocks X: = the number of dollars invested in utility stocks Maximize .12X1 + .06X: (maximize return on investment) Subject to X1 +X2 < 50,000 (limit on total investment) 3X1 -2X: < 0 (average risk cannot exceed 6) X1, X2: > 0 (non-negativity constraints) Optimal Solution: X1= $20,000 X: = $30,000 Return = S4.200 The total risk is 300.000 (9 x $20000 — 4 x $30,000), which yields an avenge risk of 6 (300,000 50,000 = 6)

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