The research of Mathematic

Marsigit's opinion:
The aim is to examine and develop mathematics. The nature of Mathematic have 3 classification. There are:
1. formal Mathematic / axiomatic Mathematic / pure Mathematic
2. applied Mathematic
3. School Mathematic / concrete Mathematic / Real Mathematic
Mathematic is a deductive system consist of definition axioms and theorem in which there is no Contradiction inside. It is very easy system to establish Mathematic.
Example:

Definition:

x₁, x₂,x₃,... Є R
Axiom:
x_i + x_i+1 Є R
x_i . x_i +1 Є R
theorem:
x_i + x_i+2 Є R
proof:
x_i + x_i+1 Є R
x_i + x_i+2 Є R
theorem:
x_i + x_i+2 Є R

1. formal Mathematic / axiomatic Mathematic / pure Mathematic
In a formal Mathematic, there are several examples in the formal Mathematic. That is:

• number theory

• group theory

• ring theory

• Euclidian geometry

• Non Euclid geometry

• Field theory

2. applied Mathematic
example: use of Pythagorean theorem to make a point of a square.

3. School Mathematic / concrete Mathematic / Real Mathematic
teachers must have the intention to observe the students. Basically the intention is to develop wareness.
According to Ebbute Straker (1995) Mathematic is:

• pattern/relationship

• problem solving

• investigation

• communication
  
  
  

APPLIED MATHEMATIC

BACKGROUND

In the trade (goods production and sale of goods) is necessary mathematical calculations that require high precision. Without math, things can not walk the trade one of them. In other words, without mathematics, we are experiencing great loss if we can not count them carefully.

Therefore, we can develop mathematics in the field of trade. We can use mathematical models in a linear inequality system to help us in the calculation of trade.

In my opinion, a linear program or a system of linear equations is a very necessary way of trade and can be used as a good solution to the problem. And I will try to help explain some examples of the use of this inequality system.

THE AIM OF RESEARCH
The purpose of research in the field of trade is to develop metematika in everyday life and to assist the traders in the trade that benefit greatly, so traders do not lose money.


TO DEVELOP METHOD
In the know how to develop mathematics in everyday life is to:

• analisis

• fenomenology

DISCUSSION

1.) Here is an example of the system of linear equations using mathematical models. The problem instance is as follows: “seribu pena matematika SMU 2 hal 287”
Price sandals A is Rp10.000,00 and the price of B is Rp8.000 each sandal A have benefit Rp750,00. Capital is available only Rp4.000.000, 00 and capacity is 450 points of sale. Determine the mathematical model of the linear program if the expected profit is the maximum.

The solution:

sandal A Sandal B

price 10.000 8.000

eg A purchase of sandals and sandal B x of y purchased, the cost of purchasing both types of sandals are: (purchase cost of capital should not exceed):
10000x +8000 y ≤ 4,000,000
5x +4 y ≤ 2000 (1)
Number sandals purchased is (should not exceed the capacity of sales):
x + y ≤ 450 (2)
given the x and y are a lot of stuff, then the value of x and y must be positive and the numbers count. Thus x and y must satisfy the following inequality.
x ≥ 0, y ≥ 0 x and y € C (3)
net profit (in dollars) are:
1000x +750 y (4)
With this expectation in net profit to the maximum.
Based on the form (1), (2), (3), (4) the mathematical model of the above issues are:
x ≥ 0, y ≥ 0, 5x +4 y ≤ 2000, x + y ≤ 450 x & y € C
the form (1000x +750 y) the maximum.

2.) A company's bags and shoes and requires a 6 element 6 a week for
respective products. Each bag requires a 2 element and 2 elements
6. if each bag produces profit Rp.3000 and every shoe produced
fortunately Rp.2000 will determine a lot of bags and shoes to be produced
to obtain maximum benefit.

Answer:
Suppose many bags are x and lots of shoes is y, then:

Ax + 2ay≤ 4a

=>x + 2y ≤ 4

2bx + 2by≤ 6b

=> x + y≤ 3

x ≥0
y ≥0

X + y =3

example : for x = 0

0 + y = 3 x + 0 = 3

Y = 3 x = 3

( 0, 3 ) ( 3, 0 )

for y = 0

X + 2y = 4

example : x = 0 y = 0

0 + 2y = 4 x + 2 . (0) = 4

2y = 4 x = 4

Y = 2 ( 4, 0 )

( 0, 2 )

Titik ( x, y )	Nilai 3000x + 2000y
( 0, 2 )	4000
( 2, 1 )	8000
( 3, 0 )	9000

Thus, the benefits will maximum when produced only 3
bag.

CONCLUTION

Can be concluded that the system of linear equations is a most appropriate way to find out the benefits of producing. We also use a linear equation in terms of another. For example search for the optimum value of certain things. That way we can understand easily how to develop mathematical models in everyday life.

BIBLIOGRAPHY

Tamponas, Husein.1999.Seribu Pena Matematika SMU. Jakarta:Erlangga

Kuntarti,dkk.2006.Matematika SMA untuk Kelas XII Program Ilmu Alam.Jakarta:Gelora Aksara Pratama.