Applications of Mathematics and Statistics Report

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Applications of Mathematics and Statistics Report

IS005

Mathematics and Statistics for Daily Life

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1st semester 2015

University of Thai Chamber of Commerce

Applications of IS005 Mathematics and Statistics for Daily Life

Applications of Algebra

Algebra is a part of Mathematics that we use the most in our life. It can apply to different fields of study cause the main idea of algebra is to find the value of variable. We can find the value of the thing that we interested in by the value of the related information. For example, in the business, sometimes you want to find the numbers of unit sold to reach the company's goal. The thing that you need to know first is related information and in this case is cost of products and selling pice per unit and the profit that the company need to earn. Then, you let the number of unit sold substitute by a variable and combine costs and sales equal to profit. The last step is using algebra to solve the equation. Look at the example below.

To determine the Profit for businesses
Suppose that Company produces a product for which the variable cost per unit is $6 and fixed cost is $80,000. Each unit has a selling price of $10, Determine the number of units that must be sold for the company to earn a profit of $60,000.

 Solution: Let q be the number of units that must be sold. (In many business problems, q represents quantity.) Then the variable cost (in dollars) is 6q. The total cost for the business is therefore 6q + 80,000. The total revenue from the sale of q units is 10q.

Profit =total revenue- total cost

60,000 =10q- (6q+ 80,000)

                                Solving gives

 60,000 =10q- 6q- 80,000

4q= 140,000

q= 35,000

                               Thus, 35,000 units must be sold to earn a profit of$60,000.

Applications of Lines

Line equation is one of the ways to present our data in the graphical form. The graphs can be positive or negative, positive linear will show us that the value of y increasing when the value of x increase and negative linear will show that the value of y decreasing when the value of x increase. And if we have two or more linear equations that are related, we can solve it to find its intersection point that is refer to the solution of them. The solutions can be one or many solutions or maybe no solution. Look at the example below, the equation about demand, supply and equilibrium.

To plot the equilibrium point to determine price and quantity of product

Equilibrium

An equation that relates price per unit and quantity demanded (supplied) is called a demand equation (supply equation). Suppose that, for product Z, the demand equation is

                                  P = -[pic 2]                                  (1)

And the supply equation is

p = [pic 3]                                         (2)

[pic 4][pic 5]

When the demand and supply curves of a product are represented on the same , the point (m,n) where the curves intersect is called the point of equilibrium. The price n, called the equilibrium price, is the price at which consumers will purchase the same quantity of a product that producers wish to sell at that price. The quantity m is called the equilibrium quantity.

To determine precisely the equilibrium point, we solve the system formed by the supply and demand equations.

P = -[pic 6]                demand equation

P = [pic 7]                        supply equation

By substituting [pic 8] for p in the demand equation, we get

[pic 9]

q=450                                        equilibrium quantity

Thus

[pic 10]

                                                        [pic 11]                                       Equilibrium price

And the equilibrium point is (450, 950). Therefore, at the price of $9.50 per unit, manufactures will produce exactly the quantity (450) of units per week that consumers will purchase at the price

[pic 12][pic 13][pic 14]

Applications of Exponential Functions

The application of functions is to create the formulas that refer to the complicated calculating problems. These formulas provide us less complicated to calculate the results. Each formula depend on the types of function that appreciate to the problems. For example, in the business,

Exponential functions are involved in Compound interest, that means the interest earned by an invested amount of money (or principal) is reinvested and also earns interest. That is, the interest is compounded into principal, and there is interest on interest. So to find compound interest easier you must create its formula. Then you put its principle and rate to find it out. Look at the example below.