library(lpSolve)

# x12 x13 x24 x25 x34 x36 x47 x57 x68

c12 <- 3
c13 <- 5
c24 <- 2
c25 <- 2
c34 <- 3
c36 <- 3
c47 <- 3
c57 <- 2
c68 <- 4

u12 <- 20
u13 <- 25
u24 <- 15
u25 <- 20
u34 <- 20
u36 <- 15
u47 <- 30
u57 <- 20
u68 <- 15

b1 <- 40
b2 <- 0
b3 <- 0
b4 <- 0
b5 <- 0
b6 <- 0
b7 <- -30
b8 <- -10

f.obj <- c(c12, c13, c24, c25, c34, c36, c47, c57, c68)

f.con <- matrix (c(1,1,0,0,0,0,0,0,0,  -1,0,1,1,0,0,0,0,0,  0,-1,0,0,1,1,0,0,0,  0,0,-1,0,-1,0,1,0,0,  0,0,0,-1,0,0,0,1,0,  0,0,0,0,0,-1,0,0,1,  0,0,0,0,0,0,-1,-1,0,  0,0,0,0,0,0,0,0,-1,  1,0,0,0,0,0,0,0,0,  0,1,0,0,0,0,0,0,0,  0,0,1,0,0,0,0,0,0,  0,0,0,1,0,0,0,0,0,  0,0,0,0,1,0,0,0,0,  0,0,0,0,0,1,0,0,0,  0,0,0,0,0,0,1,0,0,  0,0,0,0,0,0,0,1,0,  0,0,0,0,0,0,0,0,1), ncol=9, byrow=TRUE)

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

f.rhs <- c(b1,b2,b3,b4,b5,b6,b7,b8,u12,u13,u24,u25,u34,u36,u47,u57,u68)

res <-  lp("min", f.obj, f.con, f.dir, f.rhs)