Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest, and she does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund she plans to invest in is 18%, whereas the average annual return for the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, whereas 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.
a. Formulate a linear programming model for this problem.

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Parrain Parrain · Answer 1 · 2022-07-26T00:28:04+02:00

Based on the amounts that Janet Lopez has to invest in stocks and bonds, the linear programming model would be:

The return on stocks (x) is 18% and the return on bonds (y) is 6%, The objective function:

= 0.18x + 0.06y

There are constraints to watch out for:

Maximum to lose on stocks is 22% and on bonds is 5% but these are to be less than the total amount of $100,000.

0.22x + 0.05y ≤ 100,000

The total amount to invest is $72,000 which means that both bonds and stocks need to be less than this amount:

x + y ≤ 720,000

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