I'm solving a simple convex optimisation problem as follows:

import numpy as np
import cvxpy as cp
from cvxopt import solvers

#Problem: A diet problem where we minimize the cost of meal while keeping in mind the calories and vitamin constraints.

# Problem Data
vitamin_a = np.matrix([107,500,0])
calories = np.matrix([72,121,65])
cps = np.matrix([0.18,0.23,0.05]) # cost per serving

#Constructing the problem
s = cp.Variable((3,1), integer=True) # number of servings

objective = cp.Minimize(cp.matmul(cps, s))
constraints = [0<=s, 10>=s, 5000<=cp.matmul(vitamin_a, s), 50000>=cp.matmul(vitamin_a, s), 2000<=cp.matmul(calories, s), 2250>=cp.matmul(calories, s)]
prob = cp.Problem(objective, constraints)

result = prob.solve()
print(s.value)

There is this issue about the solver and I could not figure out what is wrong here. I understand that since we include "interger=True", this is a mixed integer problem as pointed in the error. Also, I get the correct solution when this condition is removed.

Error:

---------------------------------------------------------------------------
SolverError                               Traceback (most recent call last)
<ipython-input-64-b5e33f262d51> in <module>
     17 prob = cp.Problem(objective, constraints)
     18 
---> 19 result = prob.solve()
     20 print(s.value)

/usr/local/lib/python3.9/site-packages/cvxpy/problems/problem.py in solve(self, *args, **kwargs)
    471         else:
    472             solve_func = Problem._solve
--> 473         return solve_func(self, *args, **kwargs)
    474 
    475     @classmethod

/usr/local/lib/python3.9/site-packages/cvxpy/problems/problem.py in _solve(self, solver, warm_start, verbose, gp, qcp, requires_grad, enforce_dpp, **kwargs)
    964                 return self.value
    965 
--> 966         data, solving_chain, inverse_data = self.get_problem_data(
    967             solver, gp, enforce_dpp, verbose)
    968 

/usr/local/lib/python3.9/site-packages/cvxpy/problems/problem.py in get_problem_data(self, solver, gp, enforce_dpp, verbose)
    579         if key != self._cache.key:
    580             self._cache.invalidate()
--> 581             solving_chain = self._construct_chain(
    582                 solver=solver, gp=gp, enforce_dpp=enforce_dpp)
    583             self._cache.key = key

/usr/local/lib/python3.9/site-packages/cvxpy/problems/problem.py in _construct_chain(self, solver, gp, enforce_dpp)
    805         A solving chain
    806         """
--> 807         candidate_solvers = self._find_candidate_solvers(solver=solver, gp=gp)
    808         self._sort_candidate_solvers(candidate_solvers)
    809         return construct_solving_chain(self, candidate_solvers, gp=gp,

/usr/local/lib/python3.9/site-packages/cvxpy/problems/problem.py in _find_candidate_solvers(self, solver, gp)
    728                     in incorrect solutions and is not recommended.
    729                 """
--> 730                 raise error.SolverError(msg)
    731             candidates['qp_solvers'] = [
    732                 s for s in candidates['qp_solvers']

SolverError: 

                    You need a mixed-integer solver for this model. Refer to the documentation
                        https://www.cvxpy.org/tutorial/advanced/index.html#mixed-integer-programs
                    for discussion on this topic.

                    Quick fix 1: if you install the python package CVXOPT (pip install cvxopt),
                    then CVXPY can use the open-source mixed-integer solver `GLPK`.

                    Quick fix 2: you can explicitly specify solver='ECOS_BB'. This may result
                    in incorrect solutions and is not recommended.
                

I tried to use the 'ECOS_BB' solver but as warned, it didnt work( gave s.value = None). Also, when I tried to use solver='GLPK', it said solver is not installed. How do I install it?