I am given two arrays A and B of n numbers (not necessarily positive), indexed from 1 to n.
I am asked to compute an array X of n numbers between 0 and 1 (inclusive) that maximizes
A[1]×X[1] + ... + A[n]×X[n]
subject to
B[1]×X[1] + ... + B[n]×X[n] = 0
Is there a standard algorithm for solving this problem?
I searched for linear programming and for the knapsack problem, but none of them seems to fit.