Wednesday, March 19, 2014

Linear Programing



Vertices:
 (0,0)
 (6,0)
 (0,6)

Constraints
Objective Function: 
x ≥ 0
y ≥ 0
x + y ≤ 6
 C=3x +4y
C=3(0)+4(0)
C=0
C=3x +4y 
C=3(6)+4(0)
C=22
C=3x +4y
C=3(0)+4(6)
C=24 




Vertices:
 (-5,4)
 (5,4)
 (5,8)

Constraints
Objective Function: 
x ≤ 5
y ≥ 4
-2x + 5y ≤ 30
 C=2x+ 5y
C=2(-5)+5(4)
C=10
 C=2x+ 5y
C=2(5)+5(4)
C=30
 C=2x+ 5y
C=2(5)+5(8)
C=50




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




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




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



Vertices:
(3,0)
(4,3)
(0,4)           (0,2)
Constraints
Objective Function: 
x ≥ 0
2x + 3y ≥ 6 
3x - y ≤ 9
x + 4y ≤ 16
C=3x+5y
C=3(3)+5(0)
C=9
C=3x+5y
C=3(4)+5(3)
C=27
C=3x+5y
C=3(0)+5(4)
C=20
C=3x+5y
C=3(0)+5(2)
C=10


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