I would really appreciate a solution for the following exercise:
We have 3 potions A, B and C each with 3 chemicals a, b and c with the following portions respectively:

A: 10 2 5
B: 15 4 2
C: 20 3 3

By mixing potions we want to make a potion that has the following portion of
a, b and c: 15, 3 and 4.

Exact mixture is impossible to get, so for the quality of mixture er take the absolute value of the largest deviation of the chemicals from the wanted portion. For example if the portion of A, B and C in the mixture is equal, the largest deviation is 2/3. What is the portion of each potion in the best possible mixture?

we want to write this as a linear program.

thank you