Load and solve a simple 2x2 linear program

We load and solve a 2x2 linear program

#####################################
# This file is part of the          #
# Xpress-R interface examples       #
#                                   #
#   (c) 2022-2025 Fair Isaac Corporation #
#####################################
#' ---
#' title: "First LP Problem"
#' ---
#' 
#' For starters, we solve the following 2-variable model from R using the Xpress-R interface
#' 
#' $$
#' \begin{align}
#' &   \min &  x_1 +    x_2 \\
#' &        & 5 x_1 + x_2 & \geq 7 \\
#' &        &   x_1 + 4 x_2 & \geq 9 \\
#' &        & x_1, x_2 & \geq 0
#' \end{align}
#' $$
#' 
## ----first LP problem---------------------------------------------------------
suppressMessages(library(xpress))
library(magrittr)

# create a list object to hold all input
problemdata <- list()

# objective coefficients
problemdata$objcoef <- c(1,1)

# row coefficients as a single matrix object
problemdata$A <- matrix(c(5,1,1,4), nrow=2, byrow=TRUE)

# right-hand side
problemdata$rhs <- c(7,9)

# row sense
problemdata$rowtype <- c("G", "G")

# lower bounds (automatically 0 if not present)
problemdata$lb <- c(0,0)

# upper bounds(automatically inferred if not present)
problemdata$ub <- c(Inf,Inf)

# names for writing to MPS/LP files
problemdata$colname <- c("x_1", "x_2")

# Problem Name displayed when the solver solves the problem.
problemdata$probname <- "FirstExample"

#' 
#' We now load everything into a new XPRSprob 'p'. `xprs_loadproblemdata`
#' can be used to load all problem data at once into an existing or new
#' problem object. In this case, we have no existing XPRSprob object.
#' `xprs_loadproblemdata` creates one for us. For convenience and the use
#' inside pipes, xprs_loadproblemdata returns the prob pointer.
#' 
## ----Load Problem Data into new Problem---------------------------------------
p <- xprs_loadproblemdata(problemdata=problemdata)
# You may also use the equivalent
# p <- createprob()
# xprs_loadproblemdata(p, problemdata=problemdata)

#' 
#' The newly created XPRSprob object supports the `print` and `summary`
#' statements. Let's get an overview of the optimization problem loaded into p
#' 
## ----Printing the Problem-----------------------------------------------------
print(p)

#' 
#' We use `xprs_optimize` to solve the model. This again returns 'p', which can be summarized using the
#' base function `summary`
## ----Solving and Summarizing the Solution Process-----------------------------
summary(xprs_optimize(p))

#' 
#' It may be useful for further processing to convert the solution into a data frame
## ----Convert Solution into a Data Frame---------------------------------------
print(data.frame(Variable=problemdata$colname, Value=getsolution(p)$x))

#' 
#' # Using a pipe workflow
#' 
#' If you are familiar with pipes in R, you can use the following, one-line
#' workflow to obtain the solution as above. The pipe operator %>% requires
#' loading the `magrittr` package.
#' 
#' The following call creates a new problem object into
#' which the problem data is loaded. Then, it passes the newly created problem
#' object into `xprs_optimize`, and `getsolution`.
#' 
#' The result of this call is a
#' solution vector, not the problem!
#' 
## ----Using Pipe Workflows-----------------------------------------------------
pipesolution <- xprs_loadproblemdata(problemdata=problemdata) %>%
  xprs_optimize() %>%
  getsolution()
print(paste("Result of the one-liner: [", paste(pipesolution$x, collapse = ", "), "]"))