Gist Example of Optimization and Linear Programming with R

lpsolve.R

# Import lpSolve package
library(lpSolve)

#
# Set up the problem: maximize
# z = 2*x1 + 11*x2 subject to
# 2*x1 + 2*x2 <= 20
#   x1 + 2*x2 <= 12
# 3*x1 + 4*x2 <= 36
#   x1        <= 5
#   x1        >= 0
#   x2        >= 0

# Set coefficients of the objective function
f.obj <- c(2, 11)

# Set matrix corresponding to coefficients of constraints by rows
# Do not consider the non-negative constraint; it is automatically assumed
f.con <- matrix(c(2, 2,
                  1, 2,
                  3, 4,
                  1, 0,
                  1, 0,
                  0, 1), nrow = 6, byrow = TRUE)

# Set unequality signs
f.dir <- c("<=",
           "<=",
           "<=",
           "<=",
           ">=",
           ">=")

# Set right hand side coefficients
f.rhs <- c(20,
           12,
           36,
           5,
           0,
           0)

# Solve: final value (z)
lp("max", f.obj, f.con, f.dir, f.rhs) 
# Success: the objective function is 66

# Variables final values
lp("max", f.obj, f.con, f.dir, f.rhs)$solution
# x1 = 0 and x2 = 6

# Sensitivities
lp("max", f.obj, f.con, f.dir, f.rhs, compute.sens = TRUE)$sens.coef.from
lp("max", f.obj, f.con, f.dir, f.rhs, compute.sens = TRUE)$sens.coef.to