## Constraints: What restricts your decisions?

At this juncture, the ideal set of decisions is likely to be obvious. Make an infinite number of anvils and sell them all for a profit (at the risk of causing road runner extinction). Eat as much as you want of all the foods you like. Sadly, various factors will constrain your free will here. There's only so much iron available for anvils, your factories have limited capacity, and demand for anvils is not infinite. Your wallet will not support that all-steak diet, your wardrobe will not support the change in dimensions resulting from all the ice cream you can eat, and your doctor (or mother) (or both) absolutely insists that something green is mandatory (and mint ice cream does not qualify).

Your task now is to identify the aspects of the situation that will limit your decisions and express them as equations or inequalities involving your decision variables. Again, you may identify auxiliary variables during this process. If you do not have a specific accounting cost for holding inventory, you might not have identified it in the previous section. When it comes time to connect anvil production with anvil shipments, though, you may find it convenient to create inventory variables.

For strictly mathematical reasons, you will need to avoid strict inequalities. Where quantities are discrete, this is easy. "I need to make more than 50 blue anvils" (strict inequality, verboten) is equivalent to "I need to make at least 51 blue anvils" (weak inequality, perfectly legal). In other cases, it may not be so easy. "We need to make some blue paint" sounds a lot like "blue paint production $> 0$", but that's a strict inequality. Your choices are either "blue paint production $\ge 0$" (allowing the possibility that you produce no blue paint) or "blue paint production $\ge \epsilon$ where $\epsilon$ is a strictly positive parameter (a lower production limit that is the minimum amount you can live with).

I hope someone finds that helpful.