Sample Essay On Calculus

The inclusion of mathematical methods in economics is largely due to the very nature of economic processes and the specifics of the science itself. Knowledge of the quantitative relations of economic processes and phenomena is based on the economic measurements. The accuracy of the measurements is largely determines the accuracy of the final results and quantitative analysis by simulation. Therefore, a prerequisite for a spectacular use of mathematical modeling is to improve the economic gauges. Formulated economic challenge in maximizing profit commercial enterprise can also be solved by one of the developed mathematical methods. It should be noted that the optimal programming methods are used effectively to plan turnover and its structure, rations menu catering to solve various transport tasks. Models built using game theory applied to alternative solutions of problems (placement of equipment with limited space, the organization of the sale of new products, etc). Queuing systems are used for maintaining large number of buyers for the calculation processes of movement of goods. Methods for network planning and management give good results in the construction of models of large shopping centers, the creation and development of automated control systems in the trade. This list does not include all of the examples of application of mathematical methods in economics, but it shows the need for analysis using mathematical apparatus in each case.
Thus, the mathematical modeling of economic phenomena and processes is an important tool of economic analysis, which enables us to obtain a comprehensive picture of the object under study, characterize and quantify analyze its internal structure and external relations. Mathematical modeling can be used to maximize the profits of trade organizations through the establishment of differentiated trade allowances. This may be running companies suppliers, optimal range of products differentially defined level of retail prices for each product group.
Let us assume that the retailer (store) has the potential number of suppliers (wholesale warehouses, manufacturers), which are the main suppliers of goods and their subsequent implementation. At the conclusion of contracts for the supply of goods, the organization chooses the desired range of food products and potential suppliers. The main factors influencing this choice, it discounts to buyers provided by suppliers, depending on the volume of goods (the larger the volume of purchased goods, the more discount); quality of the proposed product and its manufacturer; conditions of transport (supplier could "take on" transport services and include them in the purchase price of the goods), and so on.
Trading enterprises, with the aim of maximizing profits, may waive any or supplier of any of the goods, if the supplier or product does not meet the requirements. The value of the optimum volume of the goods, in which will be able to achieve the desired turnover, and hence the desired profit, this time will be unknown. In addition, this value will be limited cash resources available at some point in Trade Organization, as well as sales area and storage space.
In the construction of a mathematical model, which aims to maximize profit trade organization with existing restrictions, all costs incurred by the trade organizations were divided into two groups: external and internal. The first group included the costs of delivery of goods from suppliers to the warehouse store, including the purchase price of these goods. These costs are largely dependent on the amount of purchased goods and from a specific provider. Internal costs are recognized fully associated with the sale of goods, including labor costs of sales personnel, social payments, amortization of commercial equipment, storage costs, packaging products, advertising expenses, etc. This type of expenditure can be determined based on accounting data for the various groups of goods using the distribution method of accounting.
The goal is to determine a level of trade allowance for the goods and, therefore, to determine the retail price for each type of product to company trade could refund the purchase price of the goods, the cost of shipping goods, distribution costs and get the maximum profit level.
 n – the number of potential suppliers of goods for the organization, I = {1, n};
q – the number of species range of goods received from suppliers,Q = {1, , q};
- a set of suppliers from which the organization can receive the k-th good,  k є Q;
,  - upper and lower limit of the selling price of the k-th good for the i-th supplier,      i є , k є Q;
- the amount of funds available to the organization for the acquisition of goods;

Introduce the following notations:

-  - volume of the k-th item, received from the i-th provider,
i є ,  k є Q,   x = ( );

 - the selling price of the k-th good received from the i-th supplier

i є ,  k є Q,  y = ( );

In addition, we consider the following functions as known:

 - the upper limit for the amount of supplies k-th product of the i-th supplier with sales price ;
S(x) - Costs, calculated on the product groups with the help of accounting and distribution method;
 - the purchase price of the k-th product from the i-th supplier in the amount of .
=- the total amount of purchased goods;

 - floor space required for the sale of goods in the amount of ;

- warehouse space required to store the goods in the amount of ;
-current floor space of store;
- current floor space of warehouse.
Thus, taking into account the limitations of the available data and can construct the following mathematical model for solving the problem of maximizing the profits of commercial enterprise: 
- the objective function is to maximize the profit of the organization             (1)

With the given constraints:

     - limit on the amount of funds that can be used by organizations to purchase goods (2)
        - Limitations on the amount of goods received from suppliers (3)
,   ,  - Limitations on the retail price determined by the trade organization (4)
- Constraints on sales area                            (5)

  - Constraints on warehouse area             (6)

This problem relates to the field of nonlinear programming, so its solution can be used various mathematical methods, and that it must be used to develop a computer program that allows to solve a number of theoretical and applied problems in the field of trade.

References

Avriel, M. (1976). Nonlinear programming: Analysis and methods. Englewood Cliffs, N.J.: Prentice-Hall.
Luenberger, D., & Luenberger, D. (1984). Linear and nonlinear programming (2nd ed.). Reading, Mass.: Addison-Wesley.
Mangasarian, O. (1969). Nonlinear programming. New York: McGraw-Hill.