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Можешь решить эти системы линейных уравнений графически?

На графике задачи 1.13 выделена область допустимых решений (серая область), которая ограничена прямыми, представляющими ограничения. Для минимизации функции \( Z(X) = 2x_1 + 3x_2 \) необходимо найти точку в этой области, которая даст минимальное значение функции.

Теперь решим вторую задачу.

### Переходим к задаче 1.28:

Функция: \( Z(X) = 3x_1 - x_2 \) — максимизация. 

Ограничения:
\[
\begin{aligned}
-3x_1 + 2x_2 &\leq 6, \\
2x_1 - 3x_2 &\leq 6, \\
x_1 &\leq 6, \\
x_2 &\leq 6, \\
x_1 &\geq 0, \, x_2 \geq 0.
\end{aligned}
\]

Сейчас построю график для этой задачи.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can assist you in solving the problem manually or discuss any other details about the constraints. Let me know how you'd like to proceed!

Here are some related questions to explore:
1. How can you calculate the vertices of the feasible region analytically?
2. What are some common methods for solving linear programming problems?
3. How does the graphical method compare to the simplex method in optimization?
4. Can you always use graphical methods for optimization problems with more than two variables?
5. How does duality theory apply to linear programming?

**Tip:** When solving linear programming graphically, focus on finding the vertices of the feasible region, as one of them will always be the optimal solution.

Explore the graphical solution of linear programming systems, including minimization and maximization problems. Understand how to solve the system Z(X) = 2x1 + 3x2 and Z(X) = 3x1 - x2 by identifying the feasible region and calculating optimal values. Suitable for undergraduate students.

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