Max: f(x_{1}, x_{2}, ..., x_{n}) s.t.: g_{1}(x_{1}, x_{2}, ..., x_{n}) ≤ c_{1} g_{2}(x_{1}, x_{2}, ..., x_{n}) ≤ c_{1} .... x_{1} ≥ 0, x_{2} ≥ 0, ..., x_{n} ≥ 0 Note: x_{1}, x_{1}, ... are "real" valued 
Max: f(x_{1}, x_{2}, ..., x_{n}) s.t.: g_{1}(x_{1}, x_{2}, ..., x_{n}) ≤ c_{1} g_{2}(x_{1}, x_{2}, ..., x_{n}) ≤ c_{1} .... x_{1} ≥ 0, x_{2} ≥ 0, ..., x_{n} ≥ 0 x_{1}, x_{2}, ..., x_{n} integer 
In other words:


Linear Program  Corresponding Integer Program 


The feasible regions of the Linear Program (LP) and Integer Program (IP) are shown in the following figure:
Explanation:


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Example:


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Idea:



We will study the branch and bound method next.