Conditional constraint LP

Question

My question is fairly basic: how can I express a conditional constraint in a LP?

Example: I have a minimization of cost of production at a company. My company either can produce up to 100 bikes with a minimum of 25 for that month or doesn't produce anything at all that month.

How could I express this as a constraint in a LP?

Answer 1

You have to extend your LP to a mixed-integer model. What you have in the example is known as a semicontinuous variable and can be written as:

$$25z\leq p\leq 100z$$ where $p$ is the production that month and $z\in\{0,1\}$ is a binary variable.