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.