3 - Linear programming

Question 1

A linear programming model (LP) has:

Answer 1

a linear objective function (to be minimized or maximized)

linear constraints that limit the degree to which the objective can be pursued

a feasible region defining valid solutions (it may be empty)

an optimal solution is a feasible solution resulting in the largest possible objective
function value when maximizing (or smallest when minimizing)

Question 2

A linear program is in standard form when:

Answer 2

the objective is a minimization

all the variables are non-negative

all the constraints are equalities

Question 3

Searching an optimal solution in linear programming

It can be shown that:

Answer 3

The feasible region for any LP will be a convex set

The feasible region for any LP has only a finite number of extreme points

Any LP that has an optimal solution has an extreme point that is optimal

Question 4

General idea of the simplex method

Answer 4