document.write( "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:
\n" ); document.write( " 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?
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Algebra.Com's Answer #66694 by bucky(2189)\"\" \"About 
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
\n" ); document.write( "analysis maybe point you to the trouble you had.
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\n" ); document.write( "Since the corporate bonds have the highest interest rate, the most money would be earned by
\n" ); document.write( "putting every cent you could into corporate bonds. Assume that you could invest all $50,000
\n" ); document.write( "in corporate bonds. At an interest rate of 0.15 (that is, 15%) you would collect $50,000 times
\n" ); document.write( "0.15 in interest ... or $7500. That sets the upper limit on the interest. We now know that
\n" ); document.write( "we can't make more than $7500 by investing the $50,000.
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\n" ); document.write( "But there is a limit on the amount of money that can be invested in corporate bonds.
\n" ); document.write( "We want to put the most that we can into them because they have the highest rate of return.
\n" ); document.write( "However, the decision has been made that no more than 1/4 of the money to be invested
\n" ); document.write( "can be put into corporate bonds. Since $50,000 is to be invested, one-fourth of that
\n" ); document.write( "amount is $12,500. Therefore, the most we can put into corporate bonds is $12,500.
\n" ); document.write( "The remainder of the $50,000 is to be invested in US Treasuries. That means that
\n" ); document.write( "$50,000 less $12,500 goes into US Treasuries, and $50,000 - $12,500 = $37,500.
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\n" ); document.write( "There were two other constraints that we need to check. We were told that a minimum of
\n" ); document.write( "$25,000 must be invested in US Treasuries, and since we plan to put $37,500 in them we
\n" ); document.write( "have met that requirement. We were also told that a minimum of $10,000 must be invested in
\n" ); document.write( "Corporate Bonds, and since we plan to put $12,500 into them, we have also met that requirement.
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\n" ); document.write( "Now all we have to do is calculate the interest ...
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\n" ); document.write( "With $37,500 invested at a rate of 0.12, the interest is $37,500*0.12 = $4,500 from US
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\n" ); document.write( "And with $12,500 invested at a rate of 0.15, the interest is $12,500*0.15 = $1,875 from
\n" ); document.write( "Corporate Bonds.
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\n" ); document.write( "The total maximum interest under the limits given in the problem is $4,500 + $1,875 = $6,375.
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\n" ); document.write( "Hope this matches what the instructor gave as the answer. (Makes sense to me, at least) and
\n" ); document.write( "I also hope this helps you to find where you went astray. \n" ); document.write( "
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