Linear Programing

Vertices:	(0,0)		(0,6)		(6,0)
Constraints	Objective Function: C=3x+4y
x ≥ 0 y ≥ 0 x + y ≤ 6	3(0)+4(0)=0 Min	3(0)+4(6)=24 Max		3(6)+4(0)=18

Vertices:	(0,4)		(0,6)		(5,4)
Constraints	Objective Function: C=2x+5y
x≤5 y≥4 2x+5y≤30	2(0)+5(4)=20

Vertices:	(1,2)		(1,8)		(5,2)
Constraints	Objective Function: C=7x+3y
x ≥ 1 y ≥ 2 6x+4y ≤38	7(1,)+3(2)=13 Min	7(1)+3(8)=31		7(5)+3(2)=41 Max

Vertices:	(0,4)		(0,8)		(6,8)
Constraints	Objective Function: C=4x+6y
x ≥ 0 y ≥ 0 -2x+3y ≤ 12	4(0)+6(4)=24 Min	4(0)+6(8)=48		4(6)+6(8)=72 Max

Vertices:	(0,0) , (0,5)		(2,3) , (8,0)
Constraints	Objective Function: C=8x+7y
x ≥ 0 y ≥ 0 4x+4y≤20 x+2y≤8	8(0)+7(0)=0 8(0)+7(5)=35 0=Min	8(2)+7(3)=37 8(8)+7(0)=64 64=Max

Vertices:	(0,4)		(3,0)		(4,3)
Constraints	Objective Function: C=3x+5y
x ≥ 0 2x+3y≥6 3x-y≤9 x+4y≤16	3(0)+5(4)=20	3(3)+5(0)=9 Min		3(4)+5(3)=27 Max