# Question

LP models are used by many Wall Street firms to select a desirable bond portfolio. The following is a simplified version of such a model. A company is considering investing in four bonds; $1 million is available for investment. The expected annual return, the worst-case annual return on each bond, and the duration of each bond are given in the file S14_83.xlsx.

The company wants to maximize the expected return from its bond investments, subject to three constraints:

• The worst-case return of the bond portfolio must be at least 8%.

• The average duration of the portfolio must be at most 6. For example, a portfolio that invests $600,000 in bond 1 and $400,000 in bond 4 has an average duration of [600,000(3) + 400,000(9)]/1,000,000 = 5.4

• Because of diversification requirements, at most 40% of the total amount invested can be invested in a single bond. Determine how the company can maximize the expected return on its investment.

The company wants to maximize the expected return from its bond investments, subject to three constraints:

• The worst-case return of the bond portfolio must be at least 8%.

• The average duration of the portfolio must be at most 6. For example, a portfolio that invests $600,000 in bond 1 and $400,000 in bond 4 has an average duration of [600,000(3) + 400,000(9)]/1,000,000 = 5.4

• Because of diversification requirements, at most 40% of the total amount invested can be invested in a single bond. Determine how the company can maximize the expected return on its investment.

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