Question

Up. Answer questions 13 to 15 using the following data: A winner of the Texas Lotto has decided to invest not more than $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 risk: Stock Estimated Return Risk Index Petrochemical 12% Utility 69% The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6. The amount invested in petrochemical is X and utility is Y. 10) The objective function is: a. Maximize 0.12 X +9X+0.69Y+4Y b. Minimize 0.12 X + 9X+0.69Y+4Y c. Maximize 0.12 X+0.69 Y d. Maximize 9x + 4y 11) Investment constraint is: a. Maximize X+Y b. X+Y<=50,000 c. X+Y>=50,000 d. X+Y=50,000 12) Constraint for the risk index is: a/ 12X+69Y<=6 b. 3X-2Y<=0 c. 9X +4Y<=6 d. None of the above

Answer 1

10. C. The objective function is to maximize the return on investment. Max 0.12X + 0.69Y.

11. B. It has decided to invest not more than $50000 per year in the stock market., So, the investment in both the stocks cannot exceed $50000. Therefore, the investment constraint is X+Y<=$50000.

12. C. Given the average risk index of the investment should not be higher than 6. So, the constraint for risk index is 9X+4Y<=6.

25. C. The linear programming model equations cannot have variables with exponential power more than 1(i.e x^{​​​​​​2}​​​​​, x^{​​​​3} etc) and two variables side by side (i.e XY, YZ etc ).

26. A. Break even point is the point at which contribution equals to fixed costs resulting in zero profit or loss. Thus, it is the level of activity at which there is neither profit nor loss.

27. C. The maximin criteria is a pessimistic criteria. It chooses the best of worst.