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Questionnaire

Sets & Set Theory: Why is it important to be able to identify sets and set theory as related to business operations?

Today’s business operations rely heavily on sets and the set theory. Such vital statistics to business like the chart of accounts are impossible to formulate without sets theory. Contemporary businesses use sets and sets theory to classify most of their financial transactions.

A good example is the chart of accounts which is often used to classify business transactions based on a variety of overlapping criteria (the concept of sets thus comes in), such as the business unit, the business department, the type of transaction, the quantity of goods and services transacted for etc. Nor in calculating the multiple accounts affected by such a transaction, each of these distinct elements become a pertinent subset of all the transactions arrived at. Similarly, sets and sets notations apply in cases where multiple factors come into play with some intersecting with each other in the final analysis. As such, without a concrete understanding of the set theory, some of these cardinal transactions would end up being double counted in the balance sheet and other financial reports.

Functions? What applications do you think functions have for the business world? Can functions be used to predict next year’s profits, or how much your company will grow?

The answer to this question is in two parts. First, it is important to emphasize that functions and the concept of functions have numerous applications in modern business operations. A good example of these applications would be the calculation of a business’s current growth rate in terms of revenue generation. If an increase in revenue is determined and the trend is expected to continue appreciating, then the strategists of such a company can easily formulate a function that demonstrates and illustrates the growth of revenue for many years to come. This allows specific estimates to be made for many years ahead, while also determining the point at which growth will stagnate and market saturation will be achieved (depreciation).

Secondly, functions are very important to business and understanding them and how they construe in very many instances of business operations is vital. Most managers base their decisions on the results generated from functions. The only way to determine how a company is fairing, how it compares to past performances, how an increase in sales will affect profits, how increased expenditure such as raw materials increase in cost will determine profitability etc, can only be calculated and plotted using functions.

Linear Equations? Why is it important to understand linear equations in business? In particular can you provide examples where the relationship between items that can be affected by management and ‘items’ that management wished to achieve or attain may be ‘linear’. Can you think of items for which the relationship in NOT linear?

The concept of linear equations is a pertinent tool of management decision making processes. Every outcome of a single business decision accrues as a direct consequence of choice made. The choices themselves are handpicked based on the five core factors of management decision making in business namely, cost, potential profitability or contribution to profits, market trends, labor availability and business situation. In all decisions, these factors interact with each other directly, meaning in a linear format. Businesses use the linear equality concept to determine profitability if there is variation in such factors as cost of production, reduction of labor, increase of capital etc.

Let us exemplify that concept. A Business X needs to determine how profitable the launch of product Y would be. Considerations would be the amount of money necessary to fund production, marketing and distribution, the availability of both personnel and machines to produce the product, the market probability of accepting the product, the trends in the market where such a product may be in great demand, and the projected profits after implementing the plan. Now, in this example, the cost, labor, machinery, and market potential have a linear relationship where one affects the other directly. Nonetheless, like in all business decisions, there are some non-linear factors added to the consideration. These constitute elements that cannot be determined precisely and that are not dependent on the product or the company. Such include how well the market will receive the product, an element that can only be approximated and not calculated linearly.

Risk? A famous economist, Franc Knight, coined a definition regarding the distinction between “risk” and “uncertainty”: He defines risk as a situation where we know the possible outcome of a particular course of action and we also know the probabilities of different outcomes (think of an example). Uncertainty is defined as a situation where we don’t know exactly all the possible outcomes of a particular course of action, not the probabilities of each outcome.
What do you think is the typical situation in the business world: risk or uncertainty?
Can you think of situations in the business world or other real life situations where you would need to estimate probabilities?

Typical business situations are neither exclusively risks, nor exclusively uncertainties. Going by Franc Knight definition, most business operations embrace both an element of uncertainty and an element of risk. Most business decisions are an estimation of probabilities, bearing a strain of risk and uncertainty.

For instance, when Coca-Cola wants to launch a new alcoholic drink, they will try to establish the probable market response to such a product. The pioneer alcoholic product from the soft drink maker might be a hit in the market, just as their plain water product (Desani) became. On the other hand, the market might react very negatively to the product such that not only the product fails, but other products are affected in sales. Given their distribution and marketing expertise, having a rich experience in producing and packaging drinks, the company would definitely know how to produce and market such a drink. The risk taken here is that they would make a profit from the launch of such a product since based on their experience; they know much of what to expect. Nonetheless, what they do not know is how the market would respond irrespective of what they find out during product tests and research studies.

If the product was to gain acceptance, the company might decide to price it very low to attract more consumers and win over the alcoholic market. A low profit margin and bulk sales would make a profit that is a risk, but there is also uncertainty of whether mere price reduction would be an incentive to attract more consumers. This is just an exemplification of how most business decisions are approximations, based on probability.

Central Tendency? From a business perspective, which measurement is more important the Mode, the Mean, or the Median? Provide examples (business related) that demonstrate the appropriateness of one of these measures and the inappropriateness of the other two in a particular situation. Can you think of situations where another one of the measures is more appropriate or relevant?

Central tendency measure are used in business to indicate a central value in a distribution of variables. Mean, median and mode are simply statistical measures that help in identifying a singular score that represents the entire distribution of numerous scores. This definition is important since, when we understand the goal of using central tendency measures as being picking out a single score that is most representative of a distribution, then the mean becomes the most appropriate.

The mean comes the closest in representing other scores in a distribution. The mean aptly describes the middle value of a set of variable data and is the most popular measure of central tendency in business, computer science and engineering. Its main advantage is that it gives a unique value and that there is always a single answer and thus very useful in comparing sets of variable data. Nonetheless, the mean is affected instances of extreme values. The median describe a middle value of a data set in a way that does not account for extreme values. It is therefore not very reliable in business comparisons. The mode is only applicable in non-numeric data or in instances that one has to identify the most popular item. It thus does not account for extreme values. Not only can mean be mode be more than one answer but it is also very in accurate in projecting a central value.

Importance of Quantitative Methods in Business: Given the readings and assignments in this course, identify and briefly discuss two concepts that you believe are best applicable to business administration.

A decision-making manager can never question the applications of most quantitative methods in daily business operations. As the gross sale revenue of any organization increase for instance, so does the applications of the quantitative business methods in making decisions. This is a true and positive correlation since for instance, increased production demands.

There are two important concepts of quantitative methods that business could not exists without today. One of this is the concept of probability. Most business decisions are made on the basis of probability and the manager can only make sound decisions if he or she understands the law of probability. Probability calculations on the basis of mutually exclusive events (OR Rule) or on the basis of Venn diagrams (events that aren’t mutually exclusive) as well as based on independent events (AND Rule) are what determines which course of action a manager pursues during decision making. Probability helps managers come up with conditional probabilities, decision trees and expected values of their operations.

Another key quantitative methods’ concept used by managers is that of time value of money. Managers usually depend on the capital provided by lenders and the profitability of such loans can only be attained if the manager can calculate both simple and compound interest accurately. Other concepts of time value of money such as discounting and present value, investment appraisal and depreciation are important in keeping a business afloat just as annuities and numerous other financial instruments are in making investment decisions. These two concepts, that of probability and that of time value of money are part of modern business practices and cannot be done without.

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