Constrained optimization.

 

Discuss a situation where you had to use constrained optimization. Explain what the constraint was, what you were trying to optimize, and how you went about making your optimal decision. Include in your discussion whether or not you achieved optimality and how you knew whether you did or not.

Sample Solution

Constrained optimization

Although there are examples of unconstrained optimizations in economics, for example finding the optimal profit, maximum revenue, minimum cost, etc., constrained optimization is one of the fundamental tools in economics and in real life. Consumers maximize their utility subject to many constrained, and one significant is their budget constraint. Even Bill Gates cannot consume everything in the world and everything he wants. The commonly used mathematical technique of constrained optimizations involves the use of Language Multiplier and Lagrange function to solve these problems followed by checking the second order conditions using Bordered Hessian. When the objective is a function of two variables, and there is only one equality constraint, the constrained optimization problem can also be solved using the geometric approach given that the optimum point is an interior optimum.

ortunities immediately draw attention to the traits he processed and how they might have contributed to his leadership style. In the early 20th century, leadership traits were studied to determine what made certain people great leaders . The theory that derived from this research was known as the “Great Man Theory”.

Trait Approach

Scholarly studies have shown that there is a wide variety of different theoretical approaches to leadership. In a number of their research papers the trait approach continues to appear and therefore it would leave you to believe that there must be credibility in this theory. From the very beginning of any literature on de Gaulle, he and his leadership style are described through his characteristic. The strong referencing of de Gaulle’s characteristics leads to identifiable traits and draw evaluation of de Gaulle through this lens.

The trait theory was one of the first systematic attempts to study leadership . It focused on identifying the innate qualities and characteristics posed by great social, political, and military leaders . It was believed that people were born with these traits and only “great people possessed them .

In the mid 20th century the approach was challenged and suggested that no consistent set of traits differentiated leaders from non-leaders across a variety of situations . Recent years have seen the resurgence in the trait approach; in short, the trait approach is alive and well . It began with the emphasis on identifying the qualities of a great person; next, it shifted to include the impact of a situation on leadership; and most recently, it has shift back to re-emphasise the critical role of traits in effective leadership .

Historian Thomas Carlyle also had a major influence on this theory of leadership, at one point stating that, “The history of the world is but the biography of great men.” According to Carlyle, effective leaders are those gifted with divine inspiration and the right characteristics . Research has proven that the “Great man” theory is flawed in some aspects. One aspect being that great leaders are born with traits that make a good leader and they cannot be taught or developed over time with experience. Sociologist Herbert Spencer suggested that the leaders were products of the society in which they lived. In The Study of Sociology, Spencer wrote, “you must admit that the genesis of a great man depends on the long series of complex influences which has produced the race in which he appears, and the social state into which that race has slowly grown….Before he can remake his society, his society must make him.”

There is evidence to support for and against the great man theory. The suggestion that some people are natural leaders and therefore must have been born with some of the traits that make a good leader. However, individuals can learn and develop traits that will make them a good leader. Being self-aware and educati

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