library(lpSolve)

# x12 x13 x21 x23 x24 x31 x32 x35 x43 x46 x53 x56
w12 <- 1
w13 <- 5
w21 <- 1
w23 <- 2
w24 <- 2
w31 <- 5
w32 <- 4
w35 <- 2
w43 <- 3
w46 <- 3
w53 <- 1
w56 <- 4

f.obj <- c(w12,w13,w21,w23,w24,w31,w32,w35,w43,w46,w53,w56)

f.con <- matrix (c(1,1,-1,0,0,-1,0,0,0,0,0,0,  -1,0,1,1,1,0,-1,0,0,0,0,0,  0,-1,0,-1,0,1,1,1,-1,0,-1,0,  0,0,0,0,-1,0,0,0,1,1,0,0,  0,0,0,0,0,0,0,-1,0,0,1,1,  0,0,0,0,0,0,0,0,0,-1,0,-1), ncol=12, byrow=TRUE)

f.dir <- c("=", "=", "=", "=","=", "=")

f.rhs <- c(1, 0, 0, 0, -1, 0)

#res <-  lp("min", f.obj, f.con, f.dir, f.rhs) # LP
res <-  lp("min", f.obj, f.con, f.dir, f.rhs, binary.vec=1:12)
# 0-1IPなので，変数1-16は2値 binary.vec = 1:12,
# 整数の場合は int.vec = 1:12
print(res$solution)
print(res)