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jack1234
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Have typed the question is latex format, here it is:
http://i.stack.imgur.com/grxgI.png
http://i.stack.imgur.com/grxgI.png
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[itex] Q'max(k)[/itex] and [itex] Q'min(k) [/itex] is the aggregated max and min [itex] k-[/itex]th attribute of a composite component...
No, not all non-linear equations can be linearized in a linear programming problem. It depends on the specific equation and the constraints of the problem. Some non-linear equations may not have a linear equivalent that accurately represents the problem.
There are a few methods for determining if a non-linear equation can be linearized in a linear programming problem. One method is to graph the equation and see if it appears to be linear. Another method is to use mathematical techniques such as substitution or transformation to rewrite the equation in a linear form.
Linearizing a non-linear equation in a linear programming problem can make the problem easier to solve and can provide more accurate solutions. It can also help to simplify the problem and make it more manageable. Additionally, many optimization algorithms are designed to work with linear equations, so linearizing a non-linear equation may open up more solution options.
Yes, there can be drawbacks to linearizing a non-linear equation in a linear programming problem. Linearizing an equation may result in a loss of accuracy or may overlook important factors in the problem. Additionally, the process of linearizing an equation can be time-consuming and may require advanced mathematical skills.
In most cases, a linearized non-linear equation can still accurately represent the original problem. However, it is important to carefully consider the constraints and assumptions made when linearizing the equation. It is also a good practice to compare solutions from the linearized equation to solutions from the original non-linear equation to ensure they are similar.