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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,


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

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I think this question is more appropriate for Math Stack Exchange: – Mike Spivey Oct 20 '10 at 16:49
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. – 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.

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

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