# The city of Konigsberg 1735 in Russia.During

The fields business relies heavily on mathematics. This is seen daily as companies usually usegraphs when publishing their annual sales and profit results. However, companies andbusinesses do not just rely on math in publishing reports, but businesses also use functionsto use calculate costs and revenue. Graphs are mainly used to show correlation betweentwo distinct items or aspects called variables, in business terms these variables include loss,profit, sales, costs, supply, demand and endless other variables. There are many differenttypes of graphs including pie charts, bar graphs, scatter plots, line graphs, area, stock, anddoughnut. Previously, the business's employees had to go through the hassle of doing it byhand, however, nowadays, with the development and outburst of technology; manycomputer softwares are currently available which resulted in the ease of constructing graphswithout much hassle which also helped in cutting down costs and saving time. Graphs andfunctions offer businesses many benefits, and are of high significance in the business world.This assignment will overlook applications of graphs and functions in business including thedemand function, marginal profit function, and the use of graphs to model profits, losses,and deficiencies. A function is a relation between 2 sets in which each element from the firstset is only related to one element from the second set.BackgroundIn mathematics, graphs are actually classified as a theory or a model of a relationship.Graphs are believed to have first come about in the foreign city of Konigsberg 1735 in Russia.During that time, the locals in that area used ponder about four land masses separated by 7bridges. This merely remained a mystery until Leonhard Euler .A mathematician born and raised in Switzerland, he is one of the founding fathers of mathematics. He additionally created strategies for tackling issues in observational space science and exhibited valuable uses of arithmetic in innovation and open undertakings. He decided the appropriate response dynamically. Furthermore, he spearheaded the field of diagram hypothesis. In his answer, he understood that the land masses highlights were unessential, so every landmass could be portrayed merely by a point. Generally, Euler decreased the issue to just after ways between the landmasses and the edges that interface these vertices. Applications1. Breakeven analysisThe first example of functions and graphs in real life is the break-even analysis. This is abusiness tool in which a company has covered up all of its costs and if it exceeds this point itcan start making profit. When calculating the break-even point there are two types of costsyou should consider. The first is the fixed costs which are costs that stay the same regardlessof the amount of units a business has produced. Examples of fixed costs are rental,employee salaries and loan payments. The other type is variable costs, these are costs thatchange depending upon the quantity produced. For example commissions paid to thesalesperson, delivery costs and employee performance bounces.In a break even graph the fixed costs is represented as a straight horizontal line usually atthe bottom of the graph. While the variable costs is represented as a straight slanted linestarting from the point the y-axis and the horizontal line meet representing the revenues .To compete the break-even graph you should draw another starlight slanted linerepresenting the sales revenue, the point at which the lines of the variable cost line and therevenues meet is the breakeven point. Then you should label the region between the twolines before the break-even point as loss and the after it as profit.2. Average costThe average cost is one of the important calculated quantities in the business world. It canbe calculated by first obtaining the total costs and then dividing it by the total quantity. Therelation between quantity and costs is referred to as the average cost function. The averagecost is the total cost divided by the quantity produced.If the derivate of the average cost if found using the quotient rule, this gives the marginalaverage cost which is the total of cost of producing one additional unit product or service.When modelling average cost and marginal cost on axes, the cost per unit is usually placedon the y-axis and the output is placed on the x-axis. The result is a falling curve.DiscussionThe advantages of break-even analysis is that it is an easy tool to use to determine thecompany's financial position during different levels of output and production. It can easilyprovide the top managers of the important milestone of breaking-even and other keyfinancial like profit, loss, revenue, margin of safety and the margin of safety. It can also beused to compare the effects of changing the prices and costs on the break-even and profitsby changing the values and calculating. And this tool is generally accurate to a large extentbut its accuracy can be improved by the use of more formulae. For all the reasonsmentioned previously it can help managers make key decisions on things like large projects.While the drawbacks and disadvantages of using break-even are that break-even does nottake into consideration semi-variable costs like utility bills. It can be useless in businessenvironments where sudden changes occur. The break-even graph considers fixed costs tobe a straight horizontal line while they can change and it also considers revenue to be linearand does not change at different levels of output. Break-even depends a lot on the accuracyof the data used in calculations, so if any wrong data is used it can lead to the wrong andmisleading conclusions. The biggest drawback remains that break-even assumes that all ofthe products produced are sold.The benefits of using the average cost method includes the fact that it is simple which makesit easy to keep up with inventory expenses. However, this also comes with a drawback,because of the simplicity, there may be uncovered costs that have not been taken intoconsideration during the process, which results in misleading judgments. Another advantageincludes saving money and costs, this is because keeping track of inventory is maderelatively easy expense can be saved on the software or employee's pay responsible forrecording inventory. On the contrary, the average cost method makes the assumption thatall the units are equal, which can be a problem when updating products.