Lisa has $100,000 to invest in 10 mutual fund alternatives. She has some self-im

Question

Lisa has $100,000 to invest in 10 mutual fund alternatives. She has some self-imposed restrictions for her investment strategy. First, she must invest all of the $100,000. For diversification, no more than $25,000 can be invested in any fund. However, if a fund is chosen for investment, then at least $10,000 must be invested in it. No more than two funds can be pure growth funds. At least one pure bond fund must be selected. The total amount invested in pure bond funds must be at least as much as the amount invested in pure growth funds.

Formulate and solve a model that will maximize Lisa’s expected annual return.

How much do you invest in Fund 2 (round to the nearest whole dollar)?

Fund Type 1 2 Expected Return Growth Growth Growth Growth Growth & Income Growth & Income Growth & Income Stock &Bond; Bond 6.99% 8.45% 7.45% 4 5 6.45% 7 6.90% 5.15% 5.08% 9 10 Bond

Explanation / Answer

Lisa has $100,000 to invest in 10 mutual fund alternatives. First, she must invest all of the $100,000. For diversification, no more than $25,000 can be invested in any fund. However, if a fund is chosen for investment, then at least $10,000 must be invested in it. No more than two funds can be pure growth funds. At least one pure bond fund must be selected. The total amount invested in pure bond funds must be at least as much as the amount invested in pure growth funds.

As Highest rate of return, she must opt for Fund 3 at 8.45 % Return say $ 10000

As per her constraint, she must opt for one pure Bond fund Fund 9 at higher rate return of 5.15% say $ 10000

Now remaining $ 80000 she can invest in growth & income Fund 5 say $ 80000 at 7.23 %

So total return expected = 10%*8.45 + 10%*5.15 + 80% * 7.23 = 7.144%

No need for any explicit investment in Fund 2

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