Here, the inquiry focuses on extending LP to Integer Programming and Mixed-Integer Programming. The answer should highlight the differences and significance of these extensions, particularly in addressing scenarios with discrete decision variables.
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Integer Programming (IP) and Mixed-Integer Programming (MIP) are optimization techniques where some or all decision variables are constrained to take only integer values, while Linear Programming (LP) deals with continuous variables. IP and MIP are used in situations where solutions must be whole numbers, making them suitable for problems involving discrete choices or resource allocation.