Using the Simplex procedure for Minimization problems
FA minimization problem can be converted to a maximization problem just by multiplying the objective function by (-1).
FOnce this is done the problem is solved exactly the same as the maximization problem
FExample:
Minimize z = x1- 3x2 2x3
Subject to:
3x1 - x2 + 2x3 £ 7
-2x1 + 4x2 + 2x3 £ 12
-4x1 + 3x2 + 8x3 £ 10
x1, x2 ³ 0
Maximize (-z) = -x1+ 3x2 + 2x3
Subject to:
3x1 - x2 + 2x3 £ 7
-2x1 + 4x2 + 2x3 £ 12
-4x1 + 3x2 + 8x3 £ 10
x1, x2 ³ 0
Max. z + x1 - 3x2 2x3 = 0
Subject to:
3x1 - x2 + 2x3 + S1 = 7
-2x1 + 4x2 + 2x3+ S2 = 12
-4x1 + 3x2 + 8x3 + S3 = 10
x1, x2, S1 , S2, S3,³ 0