3.3 and 3.4

how to ID optimal solution?

1. ID basic variables and non-basic 2. set all non-basic to zero and solve for basic

4 steps to fundamental theorme of linear programming

1. If a feasible region is bounded, then a maximum and a minimum value for the objective function exists. 2. If a feasible region is unbounded, in Quadrant I, and the objective function has only positive coefficients, then: 3. If there is no feasible region, as it is not possible for all constraints to be met simultaneously, then there is no solution to the linear programming problem. If a solution exists to a linear programming problem, then it will occur at a corner point of the feasible region. • If the objective function is optimized at a single corner point, then the linear programming problem has an optimal solution at one unique point. • If the objective function is optimized at two adjacent corner points, then it is optimized at those two points and at every point along the boundary line segment connecting the two points. Thus, the linear programming problem has an optimal solution at infinitely many points (along the boundary line segment).

5 steps for method of corners

1. Set up a linear programming problem algebraically. 2. Graph the constraints and determine the feasible region, S. 3. Identify the exact coordinates of all corner points of the feasible region, S. 4. Decide whether or not the linear programming problem will have a solution, based upon the Fundamental Theorem of Linear Programming. 5. If a solution will exist, evaluate the objective function at each corner point. The "optimal" point is the point that optimizes the objective function. If there is a 'tie' for where the optimal objective function value occurs, then there are infinitely many optimal solution points.

2. If a feasible region is unbounded, in Quadrant I, and the objective function has only positive coefficients, then:

a. A maximum value for the objective function does not exist. b. A minimum value for the objective function exists.

How to pivot?

go to most negative colome then smallest non-negative ratio row in that column

basic variables non-basic variables

single 1 with all other entries are zero all other columns are non-basic

What will standard maximization problems include?

the objective function which wil be maximized real-world non-negativity constraints all other constraints (must be <= and # can be negative)

What is the feasible region

where all constraints of a linear programming problem are satisfied.