Solving the inequality for the minimum value

Question

I am working on a programming problem that boils down to a set of equations and inequalities:

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 want to decide for values Xthat will give an absolute minimum C, given input Dand lists and Aand Bconsisting of a[0 - n]and b[0 - n ].

I am making a problem at the moment in Python, but the problem in general is language agnostic.

CLOSURE UPDATE: Coefficients are x[0 - n]limited to a set of non-negative integers.

Answer 1

linear programming. Simplex algorithm . , , .

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Answer 2

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Answer 3

, linear programming.

Answer 4

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Answer 5

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