Why in many situations must integer programming be used inst

Why in many situations, must integer programming be used instead of linear programming that allows non-integer variables?

Solution

Given  set of constraints on the variables {x1, x2...,xn} and also a function of these variables which has to be minimised or maximised, we assign some values to the variables and check for optimal solution.

If we assign integer values to variables it is called integer programming and if we assign any real value to variables it is non integer programming.

Normally we do not have an effective way of solving these constraints.

Integer programming is used instead of linear programmings as linear programming is harder than integer programming.

Assigning values to variables other than integers either in fractions or decimals lead to a cumbersome process and also mistakes in calculations are more likely to happen.

Hence the integer programming is preferred.

In some situations say when the variables are the no of products, or no of men, etc. it has to be integers in that cases, integer programming is compulsory

When time, temperature, height, weight, prices are the variables through they can be assigned any real values, integer programming makes the optimisation programming easier.