A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12 pairs of business calculus students while reasoning about an absolute extrema optimization problem situated in a profit maximization context revealed that solving this task was particularly difficult for a majority of the students. Specifically, setting up the objective function, interpreting critical numbers and extrema, verifying extrema, and distinguishing between relative extrema and absolute extrema was problematic for some of the students. Implications for instruction are included.