Matrix word problems
 

How would I set up these problems into a matrix? I can probably solve from there.

1)Jack is investing $50,000 in three mutual funds. He estimates that the money market fund will return 5% over the next year, the blue-chip fund will return 9%, and the high-tech fund 16%. He wants a total first-year return of $4000. To avoid excessive risk, he decides to invest three times as much in the money-market fund as in the high-tech fund. How much should Jack invest in each fund?

2)Suppose you work for a supplier of lawn products. The company needs to ship 600 pounds of grass fertilizer with a nitrogen content of 25%. You check the warehouse and find they don't have any 25% nitrogen fertilizer in stock. The warehouse has on hand three different types of grass fertilizer, G1, G2, G3, with nitrogen contents of 30%, 20%, and 15% respectively. Your boss says, "Figure out how to mix them to get the 600 pounds." You reply, "Boss, I've got three variables but only two equations. There's going to be a lot of solutions." The boss answers, "I don't care how you do it as long as you use full sacks. I don't want any open sacks hanging around to spill." Fertilizer G3 is in 60 pound sacks and the other two are in 30 pound sacks. List ALL of the various ways you can mix the fertilizers. (For instance, 10 sacks of G1 and 10 sacks of G2 is one way.)

okay, for the first one:
I'll call the variables M1, M2, M3 = money market, blue-chip, high-tech in that order
you've been given 3 equations

50,000 = M1 + M2 + M3
4,000 = .05*M1 + .09*M2 + .16*M3
M1 = 3*M3 or 0 = M1 - 3*M3

From this we have Ax=y where y is the matrix (or vector):

|50,000|
| 4,000|
| 0 |

A is the matrix:
| 1 1 1 |
| .05 .09 .16 |
| 1 0 -3 |

x is the matrix (or vector)
|M1|
|M2|
|M3|

you should be able to solve from there.



for problem 2:
Your two equations are:

600 = 30*G1 + 30*G2 + 60*G3
.25*600 = .3*30*G1 + .2*30*G2 + .15*60*G3

(for the second equation, it was easier to think of it in total amount of nitrogen instead of percentages which is why I did it that way)
from there you again have Ax=y
y is:
|600|
|150|

A is:
|30 30 60|
|9 6 9 |

xis:
|G1|
|G2|
|G3|

if you need any help solving them, just make the augmented matrix |A:y| and reduce it. Hope this helps if it's not already too late