I need to add the following to my LP problem:

If the amount of workers hired in period $t$ ($H_t$) is higher than 25, the hiring cost is only 1 instead of 1.2.

Example: if 30 workers are hired in period $t$, the hiring cost is equal to $25\times1.2+5\times1=35$.

Example 2: if only 2 workers are hired in period $t$, the hiring cost is equal to 2.4.

How do I translate this to a linear equation?

Kind regards,



closed as too localized by Scott Morrison Oct 20 '10 at 23:52

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I think this question is more appropriate for Math Stack Exchange: math.stackexchange.com $\endgroup$ – Mike Spivey Oct 20 '10 at 16:49
  • $\begingroup$ This violates the definition of a linear equation. Many of the theorems used in LP take that as an assumption and fail when the equations are not. The suggestion to solve it each way is a good one. If that gets prohibitive you need something more general than LP. $\endgroup$ – Ross Millikan Oct 20 '10 at 16:54

Solve it as two linear programs. The number of workers is $x$. One LP has $x\le 25$ and 1.2 in the cost function. The other one has $x\ge 25$ and $1.2\cdot 25 + (x-25)$ in the cost function.

  • 2
    $\begingroup$ The appropriateness of this question in this forum aside, Ben's suggestion is a good one. $\endgroup$ – Mike Spivey Oct 20 '10 at 17:03

Not the answer you're looking for? Browse other questions tagged or ask your own question.