(I am in the middle of my first theoretical cs course, so I apologize in advance for what is probably a stupid question.)
So, we say that some language L is in P, which means that a Turing machine can be constructed which outputs a 1 if x is in L and 0 otherwise; in addition, the machine runs in polynomial time. I understand this.
But many people say that there are certain problems in P which do not appear to me to be decision problems; for example, maximizing a function subject to linear constraints. What does it mean that "linear programming" is in P? Surely "find the maximal value" is not a decision problem?