Many Wall Street firms use LP models to select a desirable bond portfolio. The following is a simplified version of such a model. Solodrex 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 P04_56.xlsx. (The duration of a bond is a measure of the bond’s sensitivity to interest rates.) Solodrex 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 7%.

■ The average duration of the portfolio must be at most 6.5. 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.