Multiple objective Linear programming problems generation and find extreme point

As is well known, the multiobjective linear programming problems (MOLP) is given by the following form:

min Cx

Ax<=b

LB<=x<=UB

Where C is a p*n matrix, A is an m*n matrix,

b, LB, UB are vectors of dimension m, n, n resp.

In fact, I'd like to ask you 3 specific questions

1- how to generate a random MOLP problems by varying the number of variables n, the number of constraints m and the number of objectives p.

2-How to generate a subset of feasible solutions of each MOLP problem randomly generated.

3-How to find the extreme points for each MOLP problem randomly generated.

Thanks in advance

[Catalytic]

As is well known

Not really...