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Posted: November 2nd, 2022
QDA DB1 Decision Modelling Definition
Provide feedback on whether or not this is always the case.
Most real-life problems comprise of optimizing or minimizing a particular quantity subject to a number of constraints. Linear programming is one approach to this type of problem. In this instance, I am inclined to agree that this is always the case. As such, it is true that in many linear programming problems, those that are to be maximized have a bounded feasible region, and those that are to be minimized have an unbounded feasible region. This is because if the feasible region is unbounded, the objective function is minimized, and its coefficients are non-negative, and as such, generates a solution (Karloff, 2018). On the other hand, if the feasible region is bounded, the objective function is maximized, and its coefficients are negative thus generating a solution.
In your opinion, in what situations would that not be the scenario?
If the feasible region is nonempty and bounded, then the objective function achieves both a minimum and maximum value at extreme points of the feasible region. If there is an unbounded feasible region, then the objective function may or may not achieve the minimum or maximum value; nonetheless, if it achieves a minimum or maximum value, it does at an extreme point.
Explain what it means if you have an infeasible problem.
An infeasible problem denotes to a problem that lacks a solution. This problem may come about as a result of shortcomings or errors in the development or in the data that defines the problem (Eiselt & Sandblom, 2017).
Provide feedback about the pros and cons of having a minimized or a maximized feasible region, and provide input on your opinion of the data from each.
Pros
It is good for problems that are small
It leverages geometry of problem: visits feasible set vertices and checks every vertex visited for maximization
Cons
It is not that good for big problems since pivoting operations become costly. Notably, cutting plane algorithms such as Dantzig-Wolfe can at times compensate for this limitation
References
Eiselt, H., & Sandblom, C. (2017). Linear Programming and its Applications. Berlin,
Germany: Springer Science & Business Media.
Karloff, H. (2018). Linear Programming. Berlin, Germany: Springer Science & Business
Media.
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