solving an inequality smallest value

i'm operative programming problem boils down set an equation inequality:

x[0]*a[0] + x[1]*a[1] + ... x[n]*a[n] >= d
x[0]*b[0] + x[1]*b[1] + ... x[n]*b[n] =  c

i wish solve values x give comprehensive smallest c, given quarrel d lists a b consisting a[0 - n] b[0 - n ].

i'm doing problem during impulse python, nonetheless problem whole language-agnostic.

clarification update: coefficients x[0 - n] limited set non-negative integers.