hi I'm desperately trying to answer this question:
3. A couple has $40,000 to invest. As their financial consultant, you recommend they invest some money in treasury bills that yield 6%, some money in corporate bonds that yield 8%, and some money in junk bonds that yield 10%. Prepare a table showing some of the ways this couple can achieve $3,000 per year in income.


So far I realize I have to solve for a linear equation with infinite solutions but don't have the correct answers... Here's what I've got so far:

40,000 invested between 3 different securities

Option A Investment Interest
treasury 6% 10000 600
corporate 8% 10000 800
junk 10% 20000 2000
Total Interest 3400


Option B
treasury 6% 20000 1200
corporate 8% 10000 800
junk 10% 10000 1000
Total Interest 3000



Option C
treasury 6% 20000 1200
corporate 8% 1000 80
junk 10% 19000 1900
Total Interest 3180


Option D
treasury 6% 5000 300
corporate 8% 25000 2000
junk 10% 10000 1000
Total Interest 3300

I would suggest that you fix one of the variables to some value, and then see how the other two investments could be made so that the total adds to $3K. This will get you two equations in two unknowns, which you can solve. For example, fix the T-Bill amount at $20,000, which will generate $1200. That means the remaining $20K has to generate $1800. You end up with 2 equations like this:

$1800 = .08*Corp + .10*Junk
Corp + Junk = $20K

Solve, and you'll see that in this case Corp = $10K and Junk= $10.

Now try with a few different values for T-Bills, and you'll have your table.

Maybe I'm missing how this is hard. Just pick some randomly smallish numbers for two types and calculate what the third must be to make the interest equal $3000.
Interest=0.06*T+0.08*C+0.10J

Quote:

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Originally Posted by asterisk_man

Maybe I'm missing how this is hard. Just pick some randomly smallish numbers for two types and calculate what the third must be to make the interest equal $3000.
Interest=0.06*T+0.08*C+0.10J

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You're missing the fact that the total investment is $40K. Hence you need the constraint that T+C+J = 40K.