Discussion Week 7 Question 1 Comparing Graphical and Computer-Based Methods - Assignment Example

Comparing Graphical and Computer-Based Methods al Affiliation Comparing Graphical and Computer-Based Methods What does the shadow price reflect in a maximization problem? Please explain. The shadow price, in a maximization problem with an identified objective constraint, reportedly reflects “the amount that the objective function of the maximization would increase by if the constraint were relaxed by one unit” (Beggs, 2014, par. 1). This was corroborated by Spivey (2011) who expounded the concept of shadow price in a maximization problem, to wit: “For maximization problems like this one the constraints can often be thought of as restrictions on the amount of resources available, and the objective can be thought of as profit.

Then the shadow price associated with a particular constraint tells you how much the optimal value of the objective would increase per unit increase in the amount of resources available. In other words, the shadow price associated with a resource tells you how much more profit you would get by increasing the amount of that resource by one unit” (Spivey, 2011, p. 1).2. How do the graphical and computer-based methods of solving LP problems differ? In what ways are they the same? Under what circumstances would you prefer to use the graphical approach?

It was emphasized by Taylor (2010) that the graphical solution is applicable for solving LP problems with only two (2) decision variables and could be visualized by the problem-solver; while the computer-based methods allow solving problems with more than two variables and would necessitate data input requirements, either through Excel or QM for Windows. Concurrently, these two methods are similar in terms of allowing the decision-makers to evaluate the outcome or solution that was arrived at using either of the methods.

Likewise, as these methods were designed to solve LP problems, they presume that all the necessary elements or characteristics that are essential for solving LP problems must be present: the objective function (either maximize profit or minimize cost), a set of constraints, the decision variables, and finally, “linearity among all constraint relationships and the objective function” (Taylor, 2010, p. 57).The graphical approach could be preferred as the most viable approach to solve LP problems when there are limited decision variables (at most two) and when the user needs to visualize the feasible solution area, as well as the optimal solution point.

In addition, if the user is not competent or proficient with computer-based programs, the graphical approach is evidently most preferred.ReferencesBeggs, J. (2014). Shadow Price. Retrieved from About.com: Economics: http://economics.about.com/od/economicsglossary/g/shadowprice.htmSpivey, M. (2011, December 14). Shadow Price in Linear Programming. Retrieved from math.stackexchange.com: http://math.stackexchange.com/questions/91504/shadow-price-in-linear-programmingTaylor, B. I. (2010). Introduction to Management Science.

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