Question 91081: I got this wrong on a test and there wasn't time in class for the instructor to go over it...Could you show me the equations and solution...I'm sure I just made a stupid mistake:
A pension fund plans to invest up to $50,000 in US Treasury bonds yielding 12% interest per year and corporate bonds yielding 15% interest per year. The fund manager is told to invest a minimum of $25,000 in the Treasury bonds and a minimum of $10,000 in the corporate bonds with no more than 1/4 of the total investment to be in corporate bonds. How much should the manger invest in each type of bond to achieve a maximum amount of annual interest? What is the maximum interest?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Since no other tutor has tried this problem, I'll take a shot at it and you can use my
analysis maybe point you to the trouble you had.
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Since the corporate bonds have the highest interest rate, the most money would be earned by
putting every cent you could into corporate bonds. Assume that you could invest all $50,000
in corporate bonds. At an interest rate of 0.15 (that is, 15%) you would collect $50,000 times
0.15 in interest ... or $7500. That sets the upper limit on the interest. We now know that
we can't make more than $7500 by investing the $50,000.
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But there is a limit on the amount of money that can be invested in corporate bonds.
We want to put the most that we can into them because they have the highest rate of return.
However, the decision has been made that no more than 1/4 of the money to be invested
can be put into corporate bonds. Since $50,000 is to be invested, one-fourth of that
amount is $12,500. Therefore, the most we can put into corporate bonds is $12,500.
The remainder of the $50,000 is to be invested in US Treasuries. That means that
$50,000 less $12,500 goes into US Treasuries, and $50,000 - $12,500 = $37,500.
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There were two other constraints that we need to check. We were told that a minimum of
$25,000 must be invested in US Treasuries, and since we plan to put $37,500 in them we
have met that requirement. We were also told that a minimum of $10,000 must be invested in
Corporate Bonds, and since we plan to put $12,500 into them, we have also met that requirement.
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Now all we have to do is calculate the interest ...
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With $37,500 invested at a rate of 0.12, the interest is $37,500*0.12 = $4,500 from US
Treasuries.
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And with $12,500 invested at a rate of 0.15, the interest is $12,500*0.15 = $1,875 from
Corporate Bonds.
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The total maximum interest under the limits given in the problem is $4,500 + $1,875 = $6,375.
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Hope this matches what the instructor gave as the answer. (Makes sense to me, at least) and
I also hope this helps you to find where you went astray.
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