lp-solve binary package in Ubuntu Jammy amd64

 The linear programming (LP) problem can be formulated as: Solve A.x >=
 V1, with V2.x maximal. A is a matrix, x is a vector of (nonnegative)
 variables, V1 is a vector called the right hand side, and V2 is a vector
 specifying the objective function.
 .
 An integer linear programming (ILP) problem is an LP with the
 constraint that all the variables are integers. In a mixed integer
 linear programming (MILP) problem, some of the variables are integer
 and others are real.
 .
 The program lp_solve solves LP, ILP, and MILP problems. It is slightly
 more general than suggested above, in that every row of A (specifying
 one constraint) can have its own (in)equality, <=, >= or =. The result
 specifies values for all variables.
 .
 lp_solve uses the 'Simplex' algorithm and sparse matrix methods for
 pure LP problems. If one or more of the variables is declared
 integer, the Simplex algorithm is iterated with a branch and bound
 algorithm, until the desired optimal solution is found. lp_solve can
 read MPS format input files.

Source package