Maximize Profit: Investing $33K in Mutual Funds

[mtingt]

An investment broker wants to invest up to $ 33000 She can invest in two mutual funds based on their yearly average return for the 5 years ending December 31, 2009: the Franklin Natural Resources fund yielding 8% and the Oppenheimer Developing Markets A fund yielding 10% She wants to invest at least $8000 in the Franklin Natural Resources fund and no more than 13000 in the Oppenheimer Developing Markets A fund. How much should she invest in each type of fund to maximize her return?

I got the two maximizing points 20,000 and 13,000

and got $2900 for max return, and it said it was wrong, why was it wrong?

 

[Ray Vickson]

An investment broker wants to invest up to $ 33000 She can invest in two mutual funds based on their yearly average return for the 5 years ending December 31, 2009: the Franklin Natural Resources fund yielding 8% and the Oppenheimer Developing Markets A fund yielding 10% She wants to invest at least $8000 in the Franklin Natural Resources fund and no more than 13000 in the Oppenheimer Developing Markets A fund. How much should she invest in each type of fund to maximize her return?

I got the two maximizing points 20,000 and 13,000

and got $2900 for max return, and it said it was wrong, why was it wrong?

It is not wrong.

However, your description of your solution is a bit wrong: you do not have two maximizing points, you just have the single point (F,O) = (20,13) (in $000s).

RGV

 

[mtingt]

ok thanks, I put that in online and it said my Max return was wrong, is it because it said 5 years?
even if it was 5 years, I multiplied the max return by 5 and it was still wrong?

is it just me or something is wrong with the system?

 

[Ray Vickson]

The LP formulation is: let F = $000s invested in Franklin and O = $000s invested in Oppehheimer. then: the annual yield, in $000s is 80*F + 100*O, so:
max Z = 80*F + 100*O
st
F >= 8
O <= 13
O+F <= 33
O,F >= 0.

The optimal solution is F = 20, O = 13, giving Z = 2900. Then the only issue is whether or not to multiply the 2900 by 5. If some system is not accepting this solution that system is wrong or has bugs.

RGV