lpSolve to solving an Integer programming problem-CodePudding

Solving an Integer programming problem with R, the model is:

# variables: x1, x2, x3
max z = 25000x1   18000x2   31000x3

s.t.:
x1   x2   x3 = 100
5000x1   11000x2   7000x3  <= 700000
x1 >= 10
x2 >= 10
x3 >= 10

x1, x2, x3  є {0,1}

In R, I have lines as below:

library(lpSolve)

f.obj <- c(25000, 18000, 31000)

f.con <- matrix(c(1,1,1,
              5000,11000,7000,
              1,0,0,
              0,1,0,
              0,0,1), nrow = 5, byrow = TRUE)

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

f.rhs <- c(100, 700000, 10, 10, 10)

# Final value (z)
lp("max", f.obj, f.con, f.dir, f.rhs, int.vec = 1:5, all.bin = TRUE)

# Variables final values
lp("max", f.obj, f.con, f.dir, f.rhs, int.vec = 1:5, all.bin = TRUE)$solution

I expect the right answer to be (given):

Z = 2850000 when x1 = 20, x2 = 10, x3 = 70.

But above codes returns:

Error: no feasible solution found

Where went wrong, and how can I correct it? Thank you!

CodePudding user response：

According to the documentation of lpSolve the parameter all.bin specifies if all variables are binary. The correct call should be

lp("max", f.obj, f.con, f.dir, f.rhs, int.vec = 1:5, all.int = TRUE)