How do I approach binary constraint equations? I have learned about linear constraints only so far but have little idea about dealing with binary constraints. Any help would be really appreciated!
A) Suppose that we have a model with a binary decision variable “P” denoting whether or not we produce. We have another non-negative decision variable “Q” denoting the production quantity. Q can be non-zero (meaning we can produce) only if P = 1. The production capacity (if we produce) is 200 units. Find the constraint(s) that relate Q and P.
Is it Q>=0 , Q <= 200P ?
B)Suppose that we have another model with a binary decision variable “P” denoting whether or not we produce. We have another non-negative decision variable “Q” denoting the production quantity. Q can be non-zero (meaning we can produce) only if P = 1. Due to an economy of scale condition, the production can only occur if we produce at least 50 units. There is no upper capacity here. Find the constraint(s) that relate Q and P.
I am not sure how to solve this one. Please help!
Your answer to (A) is probably sufficient in context. It says that $P=0\implies Q=0$ (no production implies quantity zero). It does not say that $P=1\implies Q>0$, but usually other things in the model will make it unattractive to "turn production on" but not produce anything. If you need to make the latter implication explicit, you need a constraint of the form $Q\ge m P$ where $m > 0$ is the minimum allowable production quantity when actually producing.
For (B), add the constraint I just described with $m=50$. You still need a constraint of the form $Q \le M P$ for some constant $M > 0$, and you need to pick $M$ large enough that you can be confident no optimal solution would produce more than that much.