Question

Minimize z = 3x + 6y subject to:
4x + y ? 20
x + y ? 20
x + y ? 10
x ? 0
y ? 0 
Graph the feasibility region.
Identify all applicable corner points of the feasibility region.
Find the point(s) (x,y) that minimizes the objective function z = 3x + 6y.

Answer 1

I assume those ? marks are < and > marks

corners
(0,0)

4x+y = 20
if x = 0, y = 20
if y = 0, x = 5

x+y = 20
if x = 0 , y = 20
if y = 0 , x = 20
this one is above and beyond the others when you graph it

x+y = 10
if x = 0 , y = 10
if y = 0, x = 10

intersection of
x+y = 10
4x+y = 20
---------
-3 x = -10
x = 10/3
y = 7/3

graph those and you will see that (0,0) is the minimum of 3x+6y