# JuMP function result\_count returns 1 when infinite solutions possible, which solver to use?
**URL:** https://discourse.julialang.org/t/jump-function-result-count-returns-1-when-infinite-solutions-possible-which-solver-to-use/94880
**Category:** Optimization (Mathematical)
**Tags:** jump
**Created:** [February 19, 2023, 2:33pm UTC](https://discourse.julialang.org/t/jump-function-result-count-returns-1-when-infinite-solutions-possible-which-solver-to-use/94880 "2023-02-19T14:33:27Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@Patrik](https://discourse.julialang.org/u/Patrik)
#### Post date: [February 19, 2023, 2:33pm UTC](https://discourse.julialang.org/t/jump-function-result-count-returns-1-when-infinite-solutions-possible-which-solver-to-use/94880/1 "2023-02-19T14:33:27Z")
Consider the following model of a simple LP problem:
```julia
using JuMP, HiGHS
m = Model(HiGHS.Optimizer)
@variable(m, x1 >= 0)
@variable(m, x2 <= 0)
@objective(m, Max, 2x1-x2)
@constraint(m, c1, 8x1-4x2<=16)
@constraint(m, c2, 3x1-4x2<=12)
print(m)
#Max 2 x1 - x2
#Subject to
# c1 : 8 x1 - 4 x2 <= 16.0
# c2 : 3 x1 - 4 x2 <= 12.0
# x1 >= 0.0
# x2 <= 0.0
JuMP.optimize!(m)
#Running HiGHS 1.4.2 [date: 1970-01-01, git hash: f797c1ab6]
#Copyright (c) 2022 ERGO-Code under MIT licence terms
#Presolving model
#2 rows, 2 cols, 4 nonzeros
#2 rows, 2 cols, 4 nonzeros
#Presolve : Reductions: rows 2(-0); columns 2(-0); elements 4(-0) - Not reduced
#Problem not reduced by presolve: solving the LP
#Using EKK dual simplex solver - serial
# Iteration Objective Infeasibilities num(sum)
# 0 -7.4999893425e-01 Ph1: 2(4.75); Du: 2(0.749999) 0s
# 1 4.0000000000e+00 Pr: 0(0) 0s
#Model status : Optimal
#Simplex iterations: 1
#Objective value : 4.0000000000e+00
#HiGHS run time : 0.02
result_count(m)
# 1
println("Objective value: ", JuMP.objective_value(m))
# Objective value: 4.0
solution_summary(m)
#* Solver : HiGHS
#
#* Status
# Result count : 1
# Termination status : OPTIMAL
# Message from the solver:
# "kHighsModelStatusOptimal"
#
#* Candidate solution (result #1)
# Primal status : FEASIBLE_POINT
# Dual status : FEASIBLE_POINT
# Objective value : 4.00000e+00
# Objective bound : 4.00000e+00
# Relative gap : Inf
# Dual objective value : 4.00000e+00
#
#* Work counters
# Solve time (sec) : 1.56868e-02
# Simplex iterations : 1
# Barrier iterations : 0
# Node count : -1
println("x1 = ", JuMP.value(x1))
# x1 = 2.0
println("x2 = ", JuMP.value(x2))
# x2 = 0.0
```
The JuMP solution shows there was a optimal (understanding global) solution found however if you consider the solution `(x1,x2)=(1, -2)` then it satisfies as well the constraints and produces the same objective value of 4, clearly multiple slutions are possible
The JuMP result count is 1 and termination status reports optimality. Is it because I defined the problem as LP and not as MILP, and some computational inacuracies show, that it does not report the multiple solutions?
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [February 19, 2023, 3:44pm UTC](https://discourse.julialang.org/t/jump-function-result-count-returns-1-when-infinite-solutions-possible-which-solver-to-use/94880/2 "2023-02-19T15:44:38Z")
Since the objective gradient and the gradient of c1 are parallel, a whole face of the polytope is composed of minima. So there’s infinitely many of them 😉 An LP solver can return any of them (if you tried an interior-point method, you could get a non-corner solution). It’s up to you to analyze the results and perhaps modify your model if you’re not happy with the solution.
---
### Author:  [@Patrik](https://discourse.julialang.org/u/Patrik)
#### Post date: [February 19, 2023, 4:40pm UTC](https://discourse.julialang.org/t/jump-function-result-count-returns-1-when-infinite-solutions-possible-which-solver-to-use/94880/3 "2023-02-19T16:40:46Z")
I understand.
How would i go About extracting the info about the gradients of objective and constraint parallelism from the JuMP Interface explicitly?
I thought this kind of solution will be given by infinite number of solutions as output of the model.