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Write the following LP in Normal Form auxiliary variables to

Write the following LP in Normal Form (auxiliary variables to be included)


Minimise f(x_1, x_2) = 2x_1 - 3x_2 + 10 s.t. 2x_1 + 4x_2 lessthanorequalto 2 5x_1 - 5x_2 = 13 -x_1 + 9x_2 greaterthanorequalto -2 x_1, x_2 greaterthanorequalto 0

Solution

The problem is converted to Normal form by adding slack, surplus and artificial variables as appropiate.

Given MINIMIZE: 2 X1 -3 X2+10

2 X1 + 4 X2 2 ------------------ 1
5 X1 -5 X2 = 13 ------------------ 2
-1 X1 + 9 X2 -2------------------ 3

X1, X2 0

Normal form:

MAZIMIZE: -2 X1 + 3 X2 -10+ 0 X3 + 0 X4 + 0 X5

2 X1 + 4 X2 + 1 X3 = 2

5 X1 -5 X2 + 1 X5 = 13

1 X1 -9 X2 + 1 X4 = 2

X1, X2, X3, X4, X5 0

wher X3,X5 are Slack Variables and X4 is artificial variable

Given MINIMIZE: 2 X1 -3 X2+10

2 X1 + 4 X2 2 ------------------ 1
5 X1 -5 X2 = 13 ------------------ 2
-1 X1 + 9 X2 -2------------------ 3

X1, X2 0

  1. As the constraint 1 is of type \'\' we should add the slack variable X3.
  2. As the constraint 2 is of type \'=\' we should add the artificial variable X5.
  3. As the constraint 3 is of type \'\', and the independent term is negative or zero (the constraint is multiplied by -1), we should add the slack variable X4.

Normal form:

MAZIMIZE: -2 X1 + 3 X2 -10+ 0 X3 + 0 X4 + 0 X5

2 X1 + 4 X2 + 1 X3 = 2

5 X1 -5 X2 + 1 X5 = 13

1 X1 -9 X2 + 1 X4 = 2

X1, X2, X3, X4, X5 0

wher X3,X5 are Slack Variables and X4 is artificial variable
Write the following LP in Normal Form (auxiliary variables to be included) Minimise f(x_1, x_2) = 2x_1 - 3x_2 + 10 s.t. 2x_1 + 4x_2 lessthanorequalto 2 5x_1 - 5

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