You have 9 equations and 16 unknown values? you can solve the nine equations for 9 of the values in terms of the other 16- 9= 7. Then order the solutions according to the conditions.
How do I solve the following system of equations (and constraints?) ?
I have not touched matrix algebra in years and have just plain forgotten.
N1 = n1,1*Q1 + n1,2*Q2 + ... + n1,16*Q16
N2 = n2,1*Q1 + n2,2*Q2 + ... + n2,16*Q16
...
N8 = n8,1*Q1 + n8,2*Q2 + ... + n8,16*Q16
Q1 + Q2 + ... + Q16 = 100
Q3 > 43
Q3 > Q4
Q4 > Q5
...
Q15 > Q16
The values for Q1, Q2, Q5, N1, N2, ..., N8, and all the ni,j are known.
I want to solve for the Q.