How does a linear program solve a problem?

It solves any linear program; it detects redundant constraints in the problem formulation; it identiﬁes instances when the objective value is unbounded over the feasible region; and it solves problems with one or more optimal solutions. The method is also self-initiating.

Is the problem of linear programming in canonical form?

A problem with this structure is said to be in canonical form. This formulation might appear to be quite limited and restrictive; as we will see later, however, any linear programming problem can be transformed so that it is in canonical form. Thus, the following discussion is valid for linear programs in general.

How is the simplex method used to solve linear programs?

This procedure, called the simplex method, proceeds by moving from one feasible solution to another, at each step improving the value of the objective function. Moreover, the method terminates after a ﬁnite number of such transitions.

What’s the optimal value for the linear program Z?

Since their coefﬁcients in the objective function are negative, if either x3or x4is positive, z will be less than 20. Thus the maximum value for z is obtained when x3= x4= 0. To summarize this observation, we state the: Optimality Criterion.

Which is the feasible region of the linear programming problem?

Any v combination of (x 1;x 2) on the line 3x 1+ x 2= 120 for x 12[16;35] will provide the largest possible value z(x 1;x 2) can take in the feasible region S.20 2.4 A Linear Programming Problem with no solution. The feasible region of the linear programming problem is empty; that is, there are no values for x 1and x 2

What are the lecture notes for linear programming?

Linear Programming Lecture Notes Linear Programming: Penn State Math 484 Lecture Notes Version 1.8.3 Christopher Gri\n « 2009-2014 Licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3.0 United States License