LP problem

Write a 1600-word essay addressing each of the following points/questions. Be sure to completely answer all the questions for each bullet point. Separate each section in your paper with a clear heading that allows you to know which bullet you are addressing in that section of your paper. Support your ideas with three (3) sources in your essay. Make sure to reference the citations using the APA writing style for the essay. The cover page, page-headings or reference page do not count towards the minimum word count.
1. What are the conditions causing linear programming problems to have multiple solutions?
2. Do you prefer the corner point method or the isoprofit, isocost method? Why?
3. Explain the purpose and procedures of the simplex method.
4. What is a shadow price? How does the concept relate to the dual of an LP problem? How does it relate to the primal?

 

Sample Solution

Linear programming (LP, also known as linear optimization) is a technique for achieving the optimal result (such as highest profit or lowest cost) in a mathematical model with linear criteria. Mathematical programming is a subset of linear programming (also known as mathematical optimization). In more formal terms, linear programming is a method for optimizing a linear objective function under constraints of linear equality and inequality. A convex polytope is a set defined as the intersection of an infinite number of half spaces, each of which is determined by a linear inequality. This polyhedron’s objective function is a real-valued affine (linear) function.

However, there are a number of challenges coming from concerns about how digital technologies are used in learning. Harris et al (2009) argue that current use of technology tends to be focused on skills required by teachers to integrate these in their classrooms, rather than students’ learning needs. Also, Burden and Atkinson (2008) suggests that most digital technologies in use in the classrooms were not created as educational tools, but have been adapted by educators for pedagogical purposes.

Numerous studies have focused on the barriers faced by the institutions when they attempt to integrate digital technologies in learning, and strategies that can be employed to overcome these barriers. Hew and Bush (2007) grouped these barriers in categories such as: structure of institutions, learning environment, assessment of learning or attitudes of learners.

Therefore, an example of barrier is found in Banyard research (2006), where it was found that the relationship between the use of digital technology and academic achievement is not direct. The findings of this research suggests that there is a weak or non-existing relationship between the introduction of digital technologies and the average performance of learners on standardised tests ( Banyard et al 2006, Underwood et al 2005). Banyard resumes by saying that the value of learning technologies can only be demonstrated if the assessments were able to model the learning that took place using these technologies.

Also, the hazards of the use of digital technology are described in research such as plagia

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