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Expand Up @@ -599,6 +599,58 @@ This example presents a complete, step-by-step solution to a **Linear Programmin



$$
\
\begin{aligned}
\text{Max.} \quad & Z = 4x_1 + 3x_2 \\
\text{S.a.} \quad &
\begin{cases}
x_1 + 3x_2 \leq 7 \\
2x_1 + 2x_2 \leq 8 \\
x_1 + x_2 \leq 3 \\
x_2 \leq 2 \\
x_1 \geq 0 \text{ e } x_2 \geq 0
\end{cases}
\end{aligned}
\
$$

<br>

```latex
\
\begin{aligned}
\text{Max.} \quad & Z = 4x_1 + 3x_2 \\
\text{S.a.} \quad &
\begin{cases}
x_1 + 3x_2 \leq 7 \\
2x_1 + 2x_2 \leq 8 \\
x_1 + x_2 \leq 3 \\
x_2 \leq 2 \\
x_1 \geq 0 \text{ e } x_2 \geq 0
\end{cases}
\end{aligned}
\
```






















Expand All @@ -609,7 +661,7 @@ This example presents a complete, step-by-step solution to a **Linear Programmin
<br> -\\\\\\\k\


# VIII - [Extras Excercise]():
# IX - [Extras Excercise]():

<br>

Expand Down Expand Up @@ -1024,57 +1076,8 @@ Intersection of x_1 + 3x_2 = 7 and 2x_1 + 2x_2 = 8:

<br><br>

## **3.** [Solve the following linear programming problem using the Simplex method]():

<br>

$$
\
\begin{aligned}
\text{Max.} \quad & Z = 4x_1 + 3x_2 \\
\text{S.a.} \quad &
\begin{cases}
x_1 + 3x_2 \leq 7 \\
2x_1 + 2x_2 \leq 8 \\
x_1 + x_2 \leq 3 \\
x_2 \leq 2 \\
x_1 \geq 0 \text{ e } x_2 \geq 0
\end{cases}
\end{aligned}
\
$$

<br>

```latex
\
\begin{aligned}
\text{Max.} \quad & Z = 4x_1 + 3x_2 \\
\text{S.a.} \quad &
\begin{cases}
x_1 + 3x_2 \leq 7 \\
2x_1 + 2x_2 \leq 8 \\
x_1 + x_2 \leq 3 \\
x_2 \leq 2 \\
x_1 \geq 0 \text{ e } x_2 \geq 0
\end{cases}
\end{aligned}
\
```

<br>

## 🚜 UNDER CONSTRUTION -----







<br><br><br><br><br><br>

# IX - [Transportation Problem (Linear Programming)]()
# X - [Transportation Problem (Linear Programming)]()

<br>

Expand Down Expand Up @@ -1239,7 +1242,7 @@ These specialized algorithms are **faster** and **simpler** due to the regular s

The transportation algorithm follows the **same logic as the Simplex method**, but with **simplifications** tailored to the structure of transportation problems:

### 🔹 [1st Phase](): Initial Basic Feasible Solution
### [1st Phase](): Initial Basic Feasible Solution

We will use two methods to find a basic solution:

Expand All @@ -1250,7 +1253,7 @@ These provide starting points for optimization.

<br>

### 🔹 [2nd Phase](): Optimality Check:
### [2nd Phase](): Optimality Check:

After obtaining a feasible solution, we check for optimality using methods like:

Expand Down