Real problems solved with systems

Question

Can anybody tell me where can I find some REAL problems (i.e. form real life) that can be solved using a 3x3 system of linear equations? Or, can anybody give me an example? A solution could be a circuit in electrical engineering, but this is not very interesting, and it doesn't seem to be so real. Thank you!

Answer 1

A factory employs three classifications of worker, each type having a different wage rate: \$10/hour for $A$'s, \$15/hour for $B$'s, \$20/hour for $C$'s. Each $A$ worker works $20$ hours per week, while $B$'s and $C$'s each work $40$ hours per week. Unfortunately, some will have to be laid off. Management has decided to

1. Reduce the total number of workers by $100$.
2. Reduce the total number of hours worked per week by $3200$.
3. Reduce the total wages per week by $\$50000$.

How many A's, B's and C's will be laid off?

Answer 2

One which I deal with in on a somewhat regular basis. Treasury notes have 3 primary risk factors (called shift, twist and butterfly). These are in fact all dimension of interest rate risk. However, once you have determined the factor loading for any given security, it behaves as a linear factor.

You and your strategy team work out an ideal risk profile based on your outlook for the market and have balanced your portfolio accordingly. The next day a client gives you $10 million to be put into the fund. Pick 3 treasury notes, calculate their factor loading, and determine how much of each you need to buy to bring your exposures back to target.

Answer 3

Your computer animation programs do 3D geometric transformations before they can draw their pictures. These involve $3 \times 3$ matrices.