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The following is the sample data given:

 | id | sample_id|     x1     |    x2     |       x3        |      x4        |
 |  1 | sample1  |   .00101   | .00000    |  .00129         |  .00265        |
 |  2 | sample2  |   .00171   | .00527    |  .00527         |  .0119         |
 |  3 | sample3  |   .00125   | .00123    |  .0017          |  .00823        |
 |  4 | sample4  |   .00971   | .00420    |  .00831         |  .0441         |

$x_1$, $x_2$, $x_3$ and $x_4$ are virus found in blood samples of four different people. For the person to be healthy the combination of all of them should not be more than $0.08$ at any time.

Some virus are considered more dangerous than others. In this case $x_2$ and $x_3$ are more dangerous. So $0.6$ times $x_2$ is always more dangerous than $0.6$ times $x_1$. Though they are under same level.

We could build a better metric by adjusting the contribution of each virus to the above mentioned limit based on it's relative "danger". Furthermore, consider we want to try several different combinations of weights (factors).

Sample table of Factor weights:
 | id |             |           |                 |                |
 |  1 |   0.8       |    1.2    |       1.5       |     0.7        |
 |  2 |   1.0       |    1.0    |       1.0       |     1.0        |
 |  3 |   0.9       |    1.1    |       1.3       |     0.6        |
 |  4 |   0.0       |    1.0    |       1.0       |     1.7        |

How do I calculate factors for this? I am sorry I am new to statistics and its not very clear to me. If you could give me some hints I will try to get to the solution. Its a homework question!!! :(

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