Maximize Profit: Investing $33K in Mutual Funds

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An investment broker is looking to maximize returns by investing $33,000 in two mutual funds: the Franklin Natural Resources fund with an 8% yield and the Oppenheimer Developing Markets A fund with a 10% yield. She must invest at least $8,000 in the Franklin fund and no more than $13,000 in the Oppenheimer fund. The optimal investment strategy is to allocate $20,000 to Franklin and $13,000 to Oppenheimer, resulting in a maximum annual return of $2,900. The confusion arises regarding whether to multiply the return by 5 years; the correct approach does not require this multiplication, indicating a potential issue with the system used for calculations.
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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?
 
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mtingt said:
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
 
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?
 
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
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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