Integer Programming Differ From Those of Linear Essay

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integer programming differ from those of linear programming.

(LP), is a type of convex programming, studies the case in which the objective function f is linear and the set of constraints is specified using only linear equalities and inequalities. Integer programming is the same thing, but with whole numbers. So integer programming is used with real life solutions that must be whole numbers that cannot be broken up.

Why is "rounding-down" an LP solution a suboptimal way to solve Integer programming problems?

It may create a solution that is very far away from the original solution.

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For example, consider:

max (2x + 3z)

where x and y are both integers above

the LP solution is

x= 4.5, y= 0.75

rounding down yields

x=4, y=0, with optimal objective value z=

but the optimal solution is actually x=4, y=1, with optimal objective value z=

So, if you were trying to find a value for something….....

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