# pongo directamente los costos de fabricacion+transporte para quitar variables del medio
# (osea en vez de poner X1,X2,X3,X4 pongo directamente sus correspondientes Xij)
# vector = (x1a,x1b,x1c,x1d,x2a,x2b,x2c,x2d,x3a,x3b,x3c,x3d,x4a,x4b,x4c,x4d)

obj <- c(88,100,96,98,90,100,96,102,90,102,100,102,96,108,100,106)
res <- matrix(c(1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
                0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,
                0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,
                0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,
                1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,
                0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,
                0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,
                0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1), nrow=8, byrow=TRUE)
sig <- c("<=","<=","<=","<=",">=",">=",">=",">=")
rhs <- c(140,260,360,220,180,280,150,200)

lpSolve::lp("min", obj, res, sig, rhs)

lpSolve::lp("min", obj, res, sig, rhs)$Solution

# asi como esta no me devuelve los X. Re edito

Z <- lp("min", obj, res, sig, rhs)
X <- Z$solution

print(Z)
print(X)

# Z=78880
# X: 0   0   0 140   0 160 100   0 180 120   0  60   0   0  50   0