diff --git a/README.md b/README.md index e9e0e5c..1f3a14b 100644 --- a/README.md +++ b/README.md @@ -599,6 +599,58 @@ This example presents a complete, step-by-step solution to a **Linear Programmin +$$ +\ +\begin{aligned} +\text{Max.} \quad & Z = 4x_1 + 3x_2 \\ +\text{S.a.} \quad & +\begin{cases} +x_1 + 3x_2 \leq 7 \\ +2x_1 + 2x_2 \leq 8 \\ +x_1 + x_2 \leq 3 \\ +x_2 \leq 2 \\ +x_1 \geq 0 \text{ e } x_2 \geq 0 +\end{cases} +\end{aligned} +\ +$$ + +
+ +```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} +\ +``` + + + + + + + + + + + + + + + + + + + @@ -609,7 +661,7 @@ This example presents a complete, step-by-step solution to a **Linear Programmin
-\\\\\\\k\ -# VIII - [Extras Excercise](): +# IX - [Extras Excercise]():
@@ -1024,57 +1076,8 @@ Intersection of x_1 + 3x_2 = 7 and 2x_1 + 2x_2 = 8:

-## **3.** [Solve the following linear programming problem using the Simplex method](): - -
- -$$ -\ -\begin{aligned} -\text{Max.} \quad & Z = 4x_1 + 3x_2 \\ -\text{S.a.} \quad & -\begin{cases} -x_1 + 3x_2 \leq 7 \\ -2x_1 + 2x_2 \leq 8 \\ -x_1 + x_2 \leq 3 \\ -x_2 \leq 2 \\ -x_1 \geq 0 \text{ e } x_2 \geq 0 -\end{cases} -\end{aligned} -\ -$$ - -
- -```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} -\ -``` - -
- -## 🚜 UNDER CONSTRUTION ----- - - - - - - - -





-# IX - [Transportation Problem (Linear Programming)]() +# X - [Transportation Problem (Linear Programming)]()
@@ -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: @@ -1250,7 +1253,7 @@ These provide starting points for optimization.
-### 🔹 [2nd Phase](): Optimality Check: +### [2nd Phase](): Optimality Check: After obtaining a feasible solution, we check for optimality using methods like: