Provide a 2 pages analysis while answering the following question: Module Two. Prepare this assignment according to the guidelines found in the APA Style Guide. An abstract is required. Functions and Sets: Applications Functions are a core concept in mathematics and they are applied in almost every discipline ranging from medical to the advanced science. Business decisions are mostly based on identifying a mathematical representation of a real world scenario. For example there can be a relationship between price and demand or interest and loans. If you depict the picture of reality in your model properly then only your decisions can be successful. Mathematical functions are important tools which assist in capturing the relationship between two variables of the real world environment. Here is a generic form of function:
where q is the quantity demanded and p is the price of the product
There are various applications of functions in business domain and some of them are discussed below:
1. Quantity demanded is a function of price, if price increases than quantity demanded goes down.
2. The wages of the workers are dependant on the number of hours worked. Sales person salary is dependant on the number of units of product that he sells.
3. Total cost for a project is dependant on the amount of fixed costs and the variable costs.
4. Economic Order Quantity (EOQ) formula is also represented as a function. EOQ is the number of units in an order that minimizes the total costs. EOQ is a function of setup costs and the cost of holding inventories.
5. The concepts of present values and future values used in finance are also represented as function.
6. The depreciation and machine value are also some how related and can be represented as functions.
7. Make or Buy decisions are the most important decisions made by the managers. Managers define the models as functions and then make decision for whether to produce the materials themselves or outsource them.
8. The profit is a function of cost and revenue.
Where q = quantity sold
9. Forecasting of various variables can be represented using functions. For instance if we want to predict the next year profit then we will first find out the linear equation from the past data using regression tools and then we can simply put the value of the year for which we want to predict the profits.
Sets are fundamental concept of mathematics. A set is a well-defined collection of objects. For instance, a set of people who have defaulted on loans amounting $500,000. The set theory involves operation related to sets (union, intersection and complement etc.). These sets are also vital for business applications. For example, let’s say that,
A = set of customers buying more than two shampoo’s at a time.
B = set of customers buying a conditioner.
The set theory has a limited usage in business world but set theory concepts provide a useful vehicle for presenting and discussing probability concepts. These probability mechanisms are applied thoroughly in business world. Fuzzy set theory is also an emerging concept that is being applied now days for business applications.
Budnick, S. Frank. Applied Mathematics for Business, Economics, and the Social
Sciences. Singapore: McGraw-Hill, 1993
Barnett, A. Raymond & Michael R. Ziegler College Algebra.
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