Unary primary inequality and primary function

1. Set up x medium-sized book corners, and set up small book corners (30-x).

According to the title: 80x+50(30-x) 190030x+60(30-x) 1620

Solution 6 x 40 3

So there are 8 options:

6 medium-sized book corners and 24 small book corners;

7 medium-sized book corners and 23 small book corners;

8 medium-sized book corners and 22 small book corners;

9 medium-sized book corners and 21 small book corners;

10 medium-sized book corners and 20 small book corners;

11 medium-sized book corners and 19 small book corners;

12 medium-sized book corners and 18 small book corners;

13 medium-sized book corners and 17 small book corners;

2 The total cost of setting up is $y.

According to the title, y=860x+570(30-x).

i.e. y=290x+17100

According to the nature of the primary function, when the coefficient of x is positive, the smaller the x, the smaller the y.

The question is min y, so take the minimum value of x, that is, x = 6 The minimum cost is y = 290 * 6 + 17100 = 18840 Answer: In 1, the program cost of "forming 6 medium-sized book corners and 24 small book corners" is the lowest, and the minimum cost is 18840 yuan.

x+y=30

and two inequalities 80x+50y less than or equal to 1900; 30x+60y is less than or equal to 1620.

X belongs to [6, 40 3], then (x, y) can be (6, 24), (7, 23), (8, 22), (9, 21), (11, 19), (12, 18), (13, 17), a total of 8 species.

860x+570y=z, the lowest is 18840 yuan when (6,24) is taken properly through linear programming.

Relation: y=kx+b. Unary one-time inequality.

It is a mathematical equation, similar to a one-dimensional equation.

Contains an unknown, the number of unknowns is 1, the coefficient of the unknown is not 0, and the left and right sides are integers.

The inequality is called a one-dimensional inequality.

A one-time function. It is one of the functions, such as y=kx+b (k, b is constant, k≠0), where x is the independent variable.

y is due to the amount of disadvantage of the lesion. In particular, when b = 0, y = kx (k is constant, k ≠ 0), y is called the proportional function of x.

Nature of Inequality:

1. The same integer is added (or subtracted) on both sides of the inequality, and the direction of the inequality sign remains the same.

2. Both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality sign remains the same.

3. Both sides of the inequality are multiplied (or divided) by the same negative number, and the direction of the inequality sign remains the same.

A general way to solve a unary one-time inequality:

1. Remove the denominator.

2. Remove parentheses.

3. Move items. 4. Merge similar items.

5. Convert the coefficient of x to 1.

The subordinate relationship between a primary function and a unary primary inequality is described as follows

1. Primary function: A primary function is a kind of pretense in the function, generally in the form of y=kx+b (k, b is a constant, k≠0), where x is an independent variable and y is a dependent variable. In particular, when b = 0, y = kx (k is constant, k ≠ 0), y is called the proportional function of x.

The primary function and its image are an important part of junior high school algebra, and also the cornerstone of high school analytic geometry, and it is also the key content of the high school entrance examination.

2. Unary inequality: Unary inequality is a mathematical equation, similar to a unary equation, containing an unknown, the number of unknowns is 1, the commotion coefficient of the unknown is not 0, and the left and right sides are integer inequalities, which is called unary inequalities. The formula that connects the first with an unequal sign contains an unknown, and the number of unknowns is 1, the coefficient of the unknown is not 0, and the formula that is an integer on the left and right sides is called a one-dimensional inequality.

3. Solution: All the solutions of an inequality with unknowns make up the solution set of this inequality. The solution set of a unary inequality is a set of solutions to a unary inequality that satisfies a particular condition, and the solution set of a unary inequality and the solution set of a unary inequality are two different concepts.

They are subordinate. In general, an inequality with unknowns has an infinite number of solutions, and the set of solutions is a range that can be expressed in the simplest form of inequality.

The primary function y=kx+b, where k,b are constants and k≠0;

The unary equation kx+b=0, the unary linear inequality kx+b>0 (or 0, etc.).

The techniques for solving unary inequalities and primary functions are as follows:

1) Classification discussion method: remove the absolute value according to the positive, zero and negative fractions of the number or formula in the absolute value symbol.

2) Zero-point segmentation discussion method: It is suitable for multiple absolute values containing one letter.

3) Two-sided flat method: suitable for equations or inequalities that are non-negative on both sides.

4) Geometric meaning method: It is suitable for situations with obvious geometric significance.

The undetermined coefficient method is a method of finding an object under the condition that the form of the object is known. It is suitable for solving important problems such as finding the coordinates of points, function analytic formulas, curve equations, etc.

The concept of the inequality state late regiment:

Generally speaking, the formula that expresses the size relationship with the pure greater than sign ">" and less than the sign "<" is called an inequality. The formula that uses "≠" to indicate an unequal relationship is also an unequal form. The common domain of the analytic formula on both sides is called the domain of the inequality.

Integer inequality:

Integer inequalities are integers on both sides (i.e., unknowns are not on the denominator). Unary Inequalities: Inequalities that contain one unknown number (i.e., unary number) and the number of unknowns is one (i.e., one).

e.g. 3- x >0. In the same way, a binary inequality is an inequality that contains two unknowns (i.e., binary) and the number of unknowns is one (i.e., one). Oranges.

According to the definition, a unary linear function is, of course, y=ax+b connected by an unequal sign, containing an unknown, and the number of unknowns is 1, the coefficient of the unknown is not 0, and the formula that is an integer on the left and right sides is called a unary one-time inequality.

For example, ax+b>0 and so on.