hi this time I will post a second-class learning
materials, namely linear program matimatika hopefully you smart :)
Linear programs (linear programming) is a method
resolution of a problem where there are two activities
or more interconnected with limitations
sources. In other words, the linear program is a way to
resolve the problem through a mathematical model developed
by problems in the form of systems of equations or
linear inequality.
Problems related to the linear program is usually associated
to determine the optimum value. The optimum value can be a value
maximum or minimum value. Search the optimum value based
existing variables (eg variables x and y). Structure of program formulation
Linear is to determine the optimum value of the objective function (purpose)
shaped system with linear inequality constraints.
Linear programming developed rapidly, especially utilization
in the areas of production management, marketing, distribution, transportation,
other fields related to optimization.
After students learn a linear program, students have an understanding
and skills in the application of the system of linear inequalities
two variables. Also have skills in model making
mathematical linear program and solve it.
As an illustration, a trader with capital goods spending
Limited, to acquire merchandise that will
benefit as much as possible. In order to get
maximum profit, the trader must choose the goods
what will be purchased and how many dollars will be used to
pay for each type of merchandise selected. Thus Problem
This can be formulated and solved by using
linear program.
4.1 Linear Inequality Systems
Before the linear program studied in depth, this section
will be first on the system of linear inequalities
and the set of the completion of the inequality system
is linear.
4.1.1 P
In the previous illustration, suppose traders only
bring money for the merchandise spending 6 million dollars.
Items to be purchased are apples and mangoes.
Based on data from the previous year's sales, the merchant wants
many apples to buy twice as many mangoes. Example
variable x declared cash (in millions of dollars) will be used
buy apples. The variables y declare money (in millions of dollars) a
will be used to buy mangoes.
The amount of money to spend apple plus the amount of money to
goods expenditures should not exceed the money that was taken. In
Mathematically, the statement can be written into
2 𝑥 + 𝑦 ≤ 6.
Example mathematical expression is called the
linear inequality. Because inequality consists of two
variables (x and y), the inequality is called the
linear inequality in two variables. The general form of the
linear inequality in two variables are defined below.
DEFINITION 4.1.1:
Linear inequality in two variables is
inequalities containing two variables and has the form
𝑎 𝑥 + 𝑏 𝑦 <𝑐 (4.1.1)
with a, b, and c are real constants. Values of a and b should not btidak
both zero. Signs <can be replaced with>, ≤, or ≥.
Some examples of linear inequalities.
a. 2 𝑥 + 𝑦 <6 b. 2 𝑥 + 𝑦 ≤ 6 c. 2 𝑥 ≤ 5
d. 7 𝑥 + 3 𝑦> 210 e. 4 + 5 𝑥 𝑦 ≥ 60 f. 𝑦 ≥ 3
Viewable inequality
2 𝑥 + 𝑦 ≤ 6 (4.1.2)
Let us observe the following.
If x = 1 and y = 3 substituted into inequality (4.1.2), •
then obtained a statement
2 1 + 3 ≤ 6 or 5 ≤ 6
The statement is true, namely that "5 ≤ 6" is
true.
If x = 7 and y = 1 substituted into inequality (4.1.2), •
then obtained a statement
2 7 + 1 ≤ 6 or 15 ≤ 6
The statement is false.
If x = 3 and y = 0 substituted into inequality (4.1.2), •
then obtained a statement
2 3 + 0 ≤ 6 or 6 ≤ 6
The statement is true.
If x = 3 and y = 2 substituted into inequality (4.1.2), •
then obtained a statement
2 3 + 2 ≤ 6 ≤ 6 atau8
The statement is false.
Linear programs (linear programming) is a method
resolution of a problem where there are two activities
or more interconnected with limitations
sources. In other words, the linear program is a way to
resolve the problem through a mathematical model developed
by problems in the form of systems of equations or
linear inequality.
Problems related to the linear program is usually associated
to determine the optimum value. The optimum value can be a value
maximum or minimum value. Search the optimum value based
existing variables (eg variables x and y). Structure of program formulation
Linear is to determine the optimum value of the objective function (purpose)
shaped system with linear inequality constraints.
Linear programming developed rapidly, especially utilization
in the areas of production management, marketing, distribution, transportation,
other fields related to optimization.
After students learn a linear program, students have an understanding
and skills in the application of the system of linear inequalities
two variables. Also have skills in model making
mathematical linear program and solve it.
As an illustration, a trader with capital goods spending
Limited, to acquire merchandise that will
benefit as much as possible. In order to get
maximum profit, the trader must choose the goods
what will be purchased and how many dollars will be used to
pay for each type of merchandise selected. Thus Problem
This can be formulated and solved by using
linear program.
4.1 Linear Inequality Systems
Before the linear program studied in depth, this section
will be first on the system of linear inequalities
and the set of the completion of the inequality system
is linear.
4.1.1 P
In the previous illustration, suppose traders only
bring money for the merchandise spending 6 million dollars.
Items to be purchased are apples and mangoes.
Based on data from the previous year's sales, the merchant wants
many apples to buy twice as many mangoes. Example
variable x declared cash (in millions of dollars) will be used
buy apples. The variables y declare money (in millions of dollars) a
will be used to buy mangoes.
The amount of money to spend apple plus the amount of money to
goods expenditures should not exceed the money that was taken. In
Mathematically, the statement can be written into
2 𝑥 + 𝑦 ≤ 6.
Example mathematical expression is called the
linear inequality. Because inequality consists of two
variables (x and y), the inequality is called the
linear inequality in two variables. The general form of the
linear inequality in two variables are defined below.
DEFINITION 4.1.1:
Linear inequality in two variables is
inequalities containing two variables and has the form
𝑎 𝑥 + 𝑏 𝑦 <𝑐 (4.1.1)
with a, b, and c are real constants. Values of a and b should not btidak
both zero. Signs <can be replaced with>, ≤, or ≥.
Some examples of linear inequalities.
a. 2 𝑥 + 𝑦 <6 b. 2 𝑥 + 𝑦 ≤ 6 c. 2 𝑥 ≤ 5
d. 7 𝑥 + 3 𝑦> 210 e. 4 + 5 𝑥 𝑦 ≥ 60 f. 𝑦 ≥ 3
Viewable inequality
2 𝑥 + 𝑦 ≤ 6 (4.1.2)
Let us observe the following.
If x = 1 and y = 3 substituted into inequality (4.1.2), •
then obtained a statement
2 1 + 3 ≤ 6 or 5 ≤ 6
The statement is true, namely that "5 ≤ 6" is
true.
If x = 7 and y = 1 substituted into inequality (4.1.2), •
then obtained a statement
2 7 + 1 ≤ 6 or 15 ≤ 6
The statement is false.
If x = 3 and y = 0 substituted into inequality (4.1.2), •
then obtained a statement
2 3 + 0 ≤ 6 or 6 ≤ 6
The statement is true.
If x = 3 and y = 2 substituted into inequality (4.1.2), •
then obtained a statement
2 3 + 2 ≤ 6 ≤ 6 atau8
The statement is false.
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