SOLUTION: Find the maximum and minimum of z=11x+22y subject to x>=0, y>=0, 4x+5y<=30, 4x+3y<=20, x<=5, y<=8

Algebra ->  Inequalities -> SOLUTION: Find the maximum and minimum of z=11x+22y subject to x>=0, y>=0, 4x+5y<=30, 4x+3y<=20, x<=5, y<=8      Log On


   

Question 947643: Find the maximum and minimum of
z=11x+22y subject to x>=0, y>=0, 4x+5y<=30, 4x+3y<=20, x<=5, y<=8
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the feasible region.
4x%2B5y=30
5y=-4x%2B30
y=-%284%2F5%29x%2B6
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C-%284%2F5%29x%2B6%29
4x%2B3y=20
3y=-4x%2B20
y=-%284%2F3%29x%2B20%2F3
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C-%284%2F5%29x%2B6%2C-%284%2F3%29x%2B20%2F3%29
Find the intersection point by substituting,
%2830-5y%29%2B3y=20
-2y=-10
y=5
Then,
4x%2B3%285%29=20
4x=5
x=5%2F4
.
.
.
So then the feasible region is,

So the extrema occur at these vertices.
(0,0): Z=11x%2B22y=11%280%29%2B22%280%29=0
(0,6): Z=11x%2B22y=11%280%29%2B22%286%29=132
(5/4,5): Z=11x%2B22y=11%285%2F4%29%2B22%285%29=55%2F4%2B440%2F4=495%2F4
(5,0): Z=11x%2B22y=11%285%29%2B22%280%29=55