Question: 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

Most discrete or integer optimization problems

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

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