Linear Programming

Linear Programming

We start by understanding that:

1) Equations create linear/non linear "curves"

****2) inequalities create "plane boundaries".

{shaded regions}

OPEN VS CLOSE

boundaries

< > <>

an open circle number line a filled in dot

dotted line plane solid line

Linear programming is concerned with the answers to the questions of "Where do the boundaries of the open or closed regions intercept".

A pet store farmer has turtles and rabbits. He has room for only 100 pets. He can sell turtles for $10 each and rabboits for 30 bucks each. He decides that he must earn at least 1500 bucks to make the job worthwhile.

a) Write the inequality that respresents the total of pets?

b)Write the inequality of that represents the total profit?

c) Graph these inequalities.

d)What are some possible solutions for the farmer?

a) T + R <(less then or equal to) 100.

b)10y+30x >(greater than or equal to)

d) (25,75) ;; (100, 0) Get rid of the turtles. The rabbits make more money.