## 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