This document discusses linear programming and its use of objective functions, constraints, and corner points to solve optimization problems. Several examples are provided to illustrate objective functions with variables x and y, subject to constraints, aiming to find the corner point that maximizes or minimizes the objective function. The examples appear to be continued on subsequent screens.

1. Section 5.6 Linear Programming

2. Objective Functions in Linear Programming

4. Example

5. Example

6. Constraints in Linear Programming

7. Example

8. Example

9. Solving Problems with Linear Programming

11. Example Continued on the next screen.

12. Example Objective: 200x+150y=z Corner (x,y)

13. Example Objective: Corner (x,y)

14. Example Objective: Corner (x,y)

15. (a) (b) (c) (d)

16. (a) (b) (c) (d)