using JuMP
using GLPKMathProgInterface

m = Model(solver = GLPKSolverLP())
@variable(m,x1 >= 0)
@variable(m,x2 >= 0)
@variable(m,x3 >= 0)
@variable(m,v >= 0)

@objective(m,Max,v)
@constraint(m, 4x1+3x2+5x3 - v >= 0)
@constraint(m, 5x1+6x2 - v >= 0)
@constraint(m, 3x1+2x2+x3 - v >= 0)
@constraint(m, x1+x2+x3 == 1)

status = solve(m)

println("Objective function: ", getobjectivevalue(m))
println("x1 = ",getvalue(x1))
println("x2 = ",getvalue(x2))
println("x3 = ",getvalue(x3))