Solve the linear programming problem

Question

p=2x+2y

subject to

2x+y<=10

x+2y<=8

x,y>=0

Answer 1

2x+y=10

x + 2y = 8 ---> x = 8 - 2y

2(8-2y) + y = 10

16 - 4y + y = 10

16 - 3y = 10

-3y = -6

y = 2 --> which forces x = 8 - 2(2) = 8 - 4 = 4

the lines intersect at (4,2)

the critical points are (0,4) , (4,2), (5,0), and of course

the origin which does nothing

Objective Function G(x,y) = 2x + 2y

G(0,4) = 8 <-- min

G(4,2) = 12 <-- max

G(5,0) = 10