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

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

Answer 1

[Torsten]

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.

[Sanjib Chowdhury]

Thank you very much. Regards, -Sanjib

Answer 2

[Titus Edelhofer]

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

[Sanjib Chowdhury]

Thank you very much. Regards, -Sanjib