I want to solve a system of equations as described below.

I have the following equations.

a11X1 + a12X2 +...+ a1nXn = b1

a21X1 + a22X2 +...+ a2nXn = b2

a31X1 + a32X2 +...+ a3nXn = b3

a41X1 + a42X2 +...+ a4nXn = b4

or equivalently

a11X1 + a12X2 +...+ a1nXn - b1 = 0

a21X1 + a22X2 +...+ a2nXn - b2 = 0

a31X1 + a32X2 +...+ a3nXn - b3 = 0

a41X1 + a42X2 +...+ a4nXn - b4 = 0

with restriction

b1+b2+b3+b4 = 1, where 0 < bi < 1, for all i=1,2,3,4.

0 < aij < 1, for all i=1,2,3,4 and j=1,...,n.

0 < X_j < 1, for all j=1,...,n.

In this case, i have

B = c(b1,b2,b3,b4) is a vector.

A =

[ a11 a12 a13...a1n

a21 a22 a23...a2n

a31 a32 a33...a3n

a41 a42 a43...a4n ]

Is a matrix.

and X = (X1,X2,...,Xn) are my variables.

How can i resolve using the linprog in the software R? or resolve with another package.

Thanks.