Optimization help

Hi, I have following optimization problem:

Min: x1 + x2 +...+ x7
subject to:

x1 + x2 >= 80
x2 + x3 >= 65
x3 + x4 >= 40

all xi are ***positive integer***.

Can somebody help me in this optimization problem?

Hi.

As stated, there are no constraints on x5, x6, x7. So, these will be 0.
Try the following

  library(lpSolve)
  mat <- rbind(
    c(1, 1, 0, 0),
    c(0, 1, 1, 0),
    c(0, 0, 1, 1))
  obj <- rep(1, times=ncol(mat))
  dir <- rep(">=", times=nrow(mat))
  rhs <- c(80, 65, 40)
  out <- lp("min", objective.in=obj, const.mat=mat, const.dir=dir, const.rhs=rhs, all.int=TRUE)
  out$solution

  [1] 55 25 40  0

Hope this helps.

Petr Savicky.