Ejercicio 2 Restricciones

Ejercicio 2

Z(min) = 500X1 + 750X2

Restricciones

1. X1 + 2X2 ≥ 70
2. 2X1 + 2X2 ≥ 130
3. 4X1 + 2X2 ≥ 150
4. X1                ≥ 0
5.              X2  ≥ 0

Resolución

1. X1 = 0    →    2X2 ≥ 70

2X2 = 70    →    X2 =    →   X2 = 35[pic 1]

(X1 , X2) = (0 , 35)

X2 = 0   →   X1 ≥ 70

X1 = 70  

(X1 , X2) = (70 , 0)

1. X1 = 0    →    2X2 ≥ 130

2X2 = 130    →    X2 =    →   X2 = 65[pic 2]

(X1 , X2) = (0 , 65)

X2 = 0   →   2X1 ≥ 130

2X1 = 130  →    X1 =    →   X1 = 65[pic 3]

(X1 , X2) = (65 , 0)

1. X1 = 0    →    2X2 ≥ 150

2X2 = 150    →    X2 =    →   X2 = 75[pic 4]

(X1 , X2) = (0 , 75)

X2 = 0   →   4X1 ≥ 150

4X1 = 150  →    X1 =    →   X1 = 37.5[pic 5]

(X1 , X2) = (37.5 , 0)

1. X1 = 0[pic 6]

                    (X1 , X2) = (0 , 0)

1. X2 = 0

[pic 7][pic 8][pic 9][pic 10][pic 11][pic 12][pic 13][pic 14][pic 15][pic 16][pic 17]

[pic 18]

[pic 19][pic 20][pic 21][pic 22][pic 23][pic 24]

[pic 25][pic 26][pic 27][pic 28]

[pic 29][pic 30][pic 31]

[pic 32][pic 33]

[pic 34][pic 35]

[pic 36]

[pic 37][pic 38][pic 39]

1. F (0 , 35)        = 500(0) + 750(35)                = 26,250
2. F (70, 0)        = 500(70) + 750(0)                = 35,000
3. F (0 , 65)        = 500(0) + 750(65)                = 48,750
4. F (65 , 0)        = 500(65) + 750(0)                = 32,500
5. F (0 , 75)        = 500(0) + 750(75)                = 56,250
6. F (37.5 , 0)        = 500(37.5) + 750(0)        = 18,750

...