Mixed-Integer Linear Program (MILP) with RStudio + gMOIP Vs Gurobi

The Model with gMOIP

\[ \begin{array}{lllll} \mbox{max} & 7.75x + 10 y & & & \\ \mbox{s.t.} & -3x + 5 y & \leq & 3 \\ & 2x + 9 y & \leq & 27 \\ & 2x + 10 y & \leq & 90 \\ \end{array} \]

library(gMOIP)
A = matrix(c(-3, 2, 2, 4, 9, 10), ncol = 2, byrow = TRUE)
b = c(3, 27, 90)
obj = c(7.75, 10)  # coefficients c

Feasible region only

plotPolytope(A, b, obj, type = rep("c", ncol(A)), crit = "max", faces = rep("c", 
    ncol(A)), plotFaces = TRUE, plotFeasible = TRUE, plotOptimum = TRUE, labels = "coord") + 
    ggplot2::ggtitle("Feasible region only") + ggplot2::xlab("x") + ggplot2::ylab("y")

Solution LP max

plotPolytope(A, b, obj, type = rep("i", ncol(A)), crit = "max", faces = rep("c", 
    ncol(A)), plotFaces = TRUE, plotFeasible = TRUE, plotOptimum = TRUE, labels = "coord") + 
    ggplot2::ggtitle("Solution LP max")

Problem using Gurobi in same model

\[ \begin{array}{lllll} \mbox{obj} & 7.75x + 10 y & & & \\ \mbox{s.t.} & -3x + 5 y & \leq & 3 \\ & 2x + 9 y & \leq & 27 \\ & 2x + 10 y & \leq & 90 \\ \end{array} \]

library(prioritizr)
library(gurobi)
library(Matrix)

model <- list()
model$A <- matrix(c(-3, 2, 2, 4, 9, 10), ncol = 2, byrow = TRUE)
model$rhs <- c(3, 27, 90)
model$sense <- c("<=", "<=", "<=")
model$varnames <- c("x", "y")
obj = c(7.75, 10)
model$modelsense <- "max"
result <- gurobi(model)

Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)
Optimize a model with 3 rows, 2 columns and 6 nonzeros
Model fingerprint: 0xbddada8b
Coefficient statistics:
  Matrix range     [2e+00, 1e+01]
  Objective range  [0e+00, 0e+00]
  Bounds range     [0e+00, 0e+00]
  RHS range        [3e+00, 9e+01]
Presolve removed 3 rows and 2 columns
Presolve time: 0.00s
Presolve: All rows and columns removed
Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0   -0.0000000e+00   0.000000e+00   0.000000e+00      0s

Solved in 0 iterations and 0.00 seconds
Optimal objective -0.000000000e+00

print(result$objval)

[1] 0

print(result$x)

[1] 0 0

print(result$y)

NULL