6. Sketch the feasible region for the following system of equations:

5𝑥+2𝑦≥10

𝑥+3𝑦≥6

3𝑥+4𝑦≥12

𝑥≥0 𝑎𝑛𝑑 𝑦≥0                                                                                                                                                                             please sketch a traditiona style graph 

Here is the sketch of the feasible region for the given system of inequalities. The shaded region represents the area that satisfies all the inequalities simultaneously:

1. \( 5x + 2y \geq 10 \) (blue line)
2. \( x + 3y \geq 6 \) (green line)
3. \( 3x + 4y \geq 12 \) (red line)
4. \( x \geq 0 \) (right of the y-axis)
5. \( y \geq 0 \) (above the x-axis)

The feasible region is the gray area where all the conditions are met.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. What are the vertices of the feasible region?
2. How can we calculate the area of the feasible region?
3. Can we determine the maximum or minimum value of a function within this region?
4. How does changing the inequality signs affect the feasible region?
5. What are some real-world applications of solving such systems?

**Tip:** When solving systems of inequalities, graphing is a powerful visual tool to understand constraints and optimize solutions.

Sketch the feasible region for the following system of equations:

5𝑥 + 2𝑦 ≥ 10

𝑥 + 3𝑦 ≥ 6

3𝑥 + 4𝑦 ≥ 12

𝑥 ≥ 0 and 𝑦 ≥ 0

Please sketch a traditional style graph.

Learn how to graph the feasible region for the system of linear inequalities: 5x + 2y ≥ 10, x + 3y ≥ 6, 3x + 4y ≥ 12, with constraints x ≥ 0 and y ≥ 0. This problem involves key algebraic concepts such as graphing inequalities and determining the feasible region. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation