Can objective function of a linear programming model contain a constant term?

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Sanjib Chowdhury
Sanjib Chowdhury 2015-3-26
评论： Sanjib Chowdhury 2015-4-2
LP model Objective function: Max Z = a1x1+a2x2+a3x3+a4x4+K
where, x1,x2,x3,x4 are variables and K is a constant x1- product price, x2- product cost, x3- substitute price, x4-import price, K- transportation cost(shipping & handling charges)per unit product

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Torsten
Torsten 2015-3-26
Conjecture:
x* is optimal for
Max Z = a1x1+a2x2+a3x3+a4x4+K
if and only if x* is optimal for
Max Z = a1x1+a2x2+a3x3+a4x4
Thus it is sufficient to consider objective functions without a constant term.
Best wishes
Torsten.

更多回答（1 个）

Titus Edelhofer
Titus Edelhofer 2015-3-26
Hi Sanjib,
yes and no. Of course it can contain a constant, but this constant does not change the optimization problem or the optimal solution.
If you have a point x that realizes the maximum of
Z = a1x1+a2x2+a3x3+a4x4
then the very same point will realize the maximum of
Z = a1x1+a2x2+a3x3+a4x4+K
So for calling linprog you might forget about K ...
Titus

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