When the coefficients of an LP problem vary within given intervals, the optimal value changes as well. Thus, we first address the question of what the minimum and maximum achievable optimal values are (the so-called best and worst cases). These values are computable by one or more (even exponentially many) LP instances; the complexity depends on the particular LP form. The next issue we address is the continuity of the optimal value function, and we will also inspect the whole image of the optimal values (not only the minimum and maximum aforementioned), which can be composed of many mutually disjoint intervals. Eventually, since the computation of the minimum and maximum values is intractable, we present several approximation methods.