Objective Function
Although the standard LP model can be either the maximization or the minimization type, it is sometimes useful to convert one form to the other.The maximization of a function is equivalent to the minimization of the negative of the same function, and vice versa.For example: Max. Z = 5X1 + 2X2 + 3X3 is mathematically equivalent to Min. (-Z) = -5X1 - 2X2 - 3X3Equivalence means that for the same set of constraints the optimum values of X_{1}, X_{2} and X_{3} are the same in both cases. The only difference is that of the values of the objective functions, although equal numerically, will appear with opposite signs. Example: Write the following LP model in the standard form:Minimum: Z = 2X1 + 3X2 Minimum: Z = X1' - 2X1'' + 3X2Subject to: X1 + X2 = 10 Subject to: X'1 - 2X''1 + 3X2 = 10 -2X1' + 3X2≤ -5 2X'1 - 2X''1 - 3X2 - S2 = 5 7X1 - 4X2 ≤ 6 7X'1 - 7X''1 - 4X2 + S3 = 6 X1 Unrestricted X1', X1'', X2, S2, S3 ≥ 0 X2 ≥ 0