1. LINEAR PROGRAMMING

2. First Graph the constraints.

3. (2,0) (0,5) (1,6) (5,2) (5,0) (4,0) Second, find the vertices. Most of the intersections are easy to find, particularly the ones that have x-axis or y-axis intercepts. Also any line that intersects a horizontal or vertical line may not be too difficult.

4. (2,0) (0,5) (1,6) (5,2) (5,0) (4,0) the intersection of lines that are not horizontal or vertical may be found using the graph, or substitution, or elimination.

5. (2,0) (0,5) (1,6) (5,2) (5,0) (4,0) z = -.4( ) + 3.2( ) 16 0 2 5 4 5 5 0 0 0 0 The final step is to plug the ordered pairs into the objective function. The point that maximizes or minimizes the function is the answer. x yz MAXIMUM MINIMUM

6. (2,0) (0,5) (1,6) (5,2) (5,0) (4,0) Now, on to the calculator.

7. PRESS THE KEY and then to run INZQUALZ APPLICATION. Move the cursor over the equality symbol. make sure INEQUALZ is running.

8. These keys are activatied by the ALPHA key.

9. Enter the constraints into y= and x=. Then press

10. Press then either one of these then choose the intersection (1).

11. You can use the Point of Interest Trace to find the vertices. Press then one of these

12. Press the right and left arrows to view all of the intersections of y 1 and y 3. Press up or down arrows to change to another pair of equations. then use the left and right arrows to view those intersections. Repeat for all of the lines.

13. Now to the GREATEST THING!!! Once you have located a P-o-I, press the ordered pairs are stored in a pair of lists called INEQX AND INEQY.

14. to evaluate the OBJECTIVE FUNCTION, enter it in the next list. first, name it.

15. Move the cursor to the name and enter the objective f(x). the objective function has been evaluated and the minimum and maximum are shown. z = -.4 x + 3.2 Y

16. Another Exercise.

17. Objective Function Maximize the number of gallons mixed. G = a + b

18. Constraints The amount of Red and Blue dye limits how much paint can be mixed. Note that a and b are greater than zero.

19. Graph the constraints and find the vertices.

20. Calculator