The final dictionary for maximize x1 2x2 x3 x4 subject to

The final dictionary for

maximize x1 + 2x2 + x3 + x4

subject to

2x1 + x2 + 5x3 + x4 <= 8

2x1 + 2x2 + 4x4 <= 12

3x1 + x2 + 2x3 <=18

x1, x2, x3, x4 >= 0

is

? = 12.4 - 1.2x1 - 0.2x5 - 0.9x6 - 2.8x4

x2 = 6 - x1 - 0.5x6 - 2x4

x3 = 0.4 - 0.2x1 - 0.2x5 + 0.1x6 + 0.2x4

x7 = 11.2- 1.6x1 + 0.4x5 + 0.3x6 + 1.6x4.

(the last three variables are the slack variables).

(a) What will be an optimal solution to the problem if the objective function is changed to

3x1 + 2x2 + x3 + x4?

(b) What will be an optimal solution to the problem if the objective function is changed to

x1 + 2x2 + 0.5x3 + x4?

(c) What will be an optimal solution to the problem if the second constraint

Solution

(a) 14

(b) 12.2

(c) 16