Most discrete or integer optimization problems are NP-hard to solve, but in certain cases, we may use the linear optimization approach to approximate it. For example, we may round the decimal / fractional solutions to the nearest integer values. Discuss the various conditions that we can (or cannot) rely on the rounding-up approach. Give at least one (1) example for each scenario (i.e., Scenario 1: rounding-up can be used; Scenario 2: rounding-up cannot be used). Explain your reasoning and conclusion in detail.