objective function

Examples of objective function in the following topics:

• Drag

  • The drag force is the resistive force felt by objects moving through fluids and is proportional to the square of the object's speed.
  • Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid.
  • This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in.
  • This video walks through a single scenario of an object experiencing a drag force where the drag force is proportional to the object's velocity.
  • Relate the magnitude of drag force to the speed of an object

• Objective, constraints and alternatives

  • The objective is a function of the values and preferences of the individual agent.
  • Economic agents have a variety of objectives.
  • There are a variety of objectives that an agent might have.
  • The achievement of any objective is subject to a set of constraints.
  • The constraints and objectives can be structured in a variety of ways.

• Symmetry of Functions

  • Two objects have symmetry if one object can be obtained from the other by a transformation.
  • Two objects are symmetric to each other with respect to the invariant transformations if one object is obtained from the other by one of the transformations.
  • In the case of symmetric functions, determining symmetry is as easy as graphing the function or evaluating the function algebraically.  
  • Symmetry of a function can be a simple shift of the graph (transformation) or the function can be symmetric about a point, line or axes.
  • Functions and relations can be symmetric about a point, a line, or an axis.  

• Free-Falling Objects

  • This is because the amount of force acting on an object is a function of not only its mass, but also area.
  • Air resistance opposes the motion of an object through the air, while friction opposes motion between objects and the medium through which they are traveling.
  • Once the object is in motion, the object is in free-fall.
  • The kinematic equations for objects experiencing free fall are:
  • Describes how to calculate the time for an object to fall if given the height and the height that an object fell if given the time to fall.

• Marketing objectives

  • Examples of objectives might be:
  • Having set the objectives for the company, both at the corporate level and the business level, the company can now develop a detailed program of functional activities to achieve the objectives.
  • employed throughout this text, each of the functional elements (e.g. finance, human resources, research) must be considered jointly.
  • Ultimately, this coordination between business functions is contingent on the market entry strategy employed as well as the degree of standardization or customization deemed.
  • Having integrated at the function level, we next consider integration of the marketing mix elements.

• Nouns as Subjects and Objects

  • An object is the recipient of an action.
  • Phrased this way, it becomes clear that the dog is the indirect object and the bone is the direct object.
  • Not all verbs require objects.
  • In this sign saying "Do not feed the coyotes", are coyotes the subject, the object, or the indirect object?
  • (Answer: They are the direct object.)

• Pronouns as Subjects and Objects

  • Pronouns can be the subject or the object of a sentence.
  • Pronouns can act as both subjects and objects.
  • Personal object pronouns are me, you, him, her, it, us, them.
  • Therefore, they are object pronouns.
  • Their forms are determined primarily by their grammatical function or antecedent rather than by person.

• Defining the Marketing Objectives

  • The marketing objectives must be based on the company's financial objectives.
  • The marketing objectives must usually be based, above all, on the organization's financial objectives.
  • Set measurable financial and marketing objectives.
  • The financial objectives are revenue, profits, and return on assets.
  • The "let's copy last year's budget" mentality is prevalent in many organizations because it is the easy way out of a not so glamorous function.

• By Functional Group

  • A particular functional group will almost always display its characteristic chemical behavior when it is present in a compound.
  • Because of this, the discussion of organic reactions is often organized according to functional groups.
  • The following table summarizes the general chemical behavior of the common functional groups.
  • For reference, the alkanes provide a background of behavior in the absence of more localized functional groups.
  • This is not surprising, since the three remaining categories provide only a coarse discrimination (comparable to identifying an object as animal, vegetable or mineral).

• Transformations of Functions

  • Transformations alter a function while maintaining the original characteristics of that function.
  • A reflection of a function causes the graph to appear as a mirror image of the original function.  
  • Let the function in question be $f(x) = x^5$.  
  • A rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation.  
  • If we rotate this function by 90 degrees, the new function reads: