Ejemplo de programación lineal

Max Z= 3x+2y

2x + 3y ≤12---------------------2x+3y=12

2x + y ≤ 8--------------------------2x+y=8

X ≥ 0

Y ≥ 0

2(0)+3(y)=12      3y=12       Y=12/3 =4   (0,4)

2x + 3(0)=12       2x=12      x= 12/2 =6   (6,0)

2(0) + y = 8         y=8            (0,8)

2 x + 0 = 8        2x=8            x= 8/2= 4  (4,0)

2x +3y =12

2x+ y= 8

Y=8-2x

2x +3 (8-2x) =12

2x +24 – 6x =12

4x + 24= 12

-4x = 12-24

-4x = -12

X= -12/-4

X= 3

Y= 8 – 2 (3)

Y= 8 – 6

Y = 2

= (3,2)

1.        3x + 2y

3(3) + 2(2) = 9 + 4 =13

2.       3x + 2y

3(4) + 2(0) =12

3.       3x + 2y

3(0) + 2(4) = 8