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Why are integer programming problems more difficult to solve than linear programming problems?
In both cases the constraints are used to produce an n-dimensional simplex which represents the "feasible region". In the case of linear programming this is the feasible region. But that is not the case for integer programming since only those points within the region for which the variables are integer are feasible.The objective function is then used to find the maximum or minimum - as required. In the case of a linear programming problem, the solution must lie on one of the vertices (or along one line in 2-d, plane in 3-d etc) of the simplex and so is easy to find. In the case of integer programming, the optimal solution so found may contain one or more variables that are not integer and so it is necessary to examine all the points in the immediate neighbourhood and evaluate the objective function at each of these points. This last requirement makes integer programming solutions more difficult to find.
What are the scope of linear programming?
Linear programming can be used to solve problems requiring the optimisation (maximum or minimum) of a linear objective function when the variables are subject to a linear constraints.
What is the set of values that solve a system of equations called?
Depending on the context, the "feasible region" or "solution set".
How do you solve a two variable inequality?
The simplest way is probably to plot the corresponding equality in the coordinate plane. One side of this graph will be part of the feasible region and the other will not. Points on the line itself will not be in the feasible region if the inequality is strict (< or >) and they will be if the inequality is not strict (≤ or ≥). You may be able to rewrite the inequality to express one of the variables in terms of the other. This may be far from simple if the inequality is non-linear.
How do you solve a fixed cost problem?
Fixed Cost Problem is a kind of the Mixed Linear Programming Problem(MILP).Also, MILP is a Parametric Quadratic Concave Programming Problem. The optimal solution is existence of vertix set of the domain set. Then, you can use the domain cutting method.
