SOLUTION: If the point (2,2) is in the feasible set and the vertices of the feasible set are (0,0), (0,15), (5,15), (16,4), and (12,0), then determine the system of linear inequalities that

Algebra ->  Inequalities -> SOLUTION: If the point (2,2) is in the feasible set and the vertices of the feasible set are (0,0), (0,15), (5,15), (16,4), and (12,0), then determine the system of linear inequalities that       Log On


   

Question 1137625: If the point (2,2) is in the feasible set and the vertices of the feasible set are (0,0), (0,15), (5,15), (16,4), and (12,0), then determine the system of linear inequalities that created the feasible set.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a picture of the feasibility region:



The feasibility region is below the red and green lines and above the blue line.

The equation of the red line is obviously y=15.

A bit of algebra with the given points shows that the equation of the green line is y=-x+20 and the equation of the blue line is y=x-12.

Since the feasibility region is below the red and green lines and above the blue line, the inequalities are

y+%3C=+15
y+%3C=+-x%2B20
y+%3E=+x-12

The inequalities would probably be given in Ax+By form; that would be

y+%3C=+15
x%2By+%3C=+20
x-y+%3C=+12

(Note with the given information being the corners of the feasibility region, we can't tell whether the inequalities are "<" or "<=".)