7.6 linear programming

Here are what I learnt today in class:

Linear Programming:

Steps to solve linear programming problems:

1. Read the problem carefully

2. Write the constraints 

    (Vocabulary: constraint ->a system of linear inequalities)

3 . Graph the inequalities. Find the feasible region.

    (Vocabulary: feasible region-> region where every point satisfies the inequalities) 

4. Calculate the vertices of the inequalities by finding the intersection point(s)

5. Plug the vertices back into the function 

6. Find the maximum or minimum value

And let's do a problem!

Example:

Find the maximum value of z = 2x+3y

                              Subject to such constraints: x>= 0

                                                                          y>=0

                                                                          x+2y<=4

                                                                          x-y<=1

Solution: the constraints are shown in the pic. The four vertices:

              (0,0): z = 0

              (1,0): z = 3

              (2,1): z = 8

              (0,2): z = 4

Thus, the max is 8 when x= 2 and y= 1

 

A lot of work, right? 

Are you skilled enough to tackle another one?