Janet Lopez is establishing an investment portfolio that wil

Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest and does not want the portfolio to include more than 65% stock. The annual return on the stock fund she plans to invest is 18%, while the average return on the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, while the most she could lose in the bond fund is 5%. To reduce her risk she wants to limit her potential maximum losses to $100,000. Formulate as a Linear Programming problem.

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Solution

Let x = Investment in Shares Let y = Investment in Bonds Objective funtion Profit function = 18%*X + 6%*Y Constraints X >= 0 Y >= 0 X=<65%*(X+Y) X + Y =< $720,000 22%*X + 5%*Y =< $100,000 On solving equations Eqn 1 X + Y =720,000 Eqn 2 .22X + .05Y = 100,000 Multiplying Eqn 1 with .22 Eqn 3 .22X + .22Y = 158,400 Eqn 2 .22X + .05Y = 100,000 Subtract Eqn 3 and 2 .17Y = 58,400 Y = 343,529 X = 376,471