Add files via upload

Signed-off-by: Fabiana 🚀  Campanari <113218619+FabianaCampanari@users.noreply.github.com>

Author: FabianaCampanari

class__11 -Designation/Exer_1a-Excel-Solver/Exerc_1a-Excel-Solver.md

@@ -0,0 +1,148 @@
+
+
+
+# Exercise 1:  Problem in Excel: Step-by-Step Solution
+
+This guide shows how to solve the assignment problem from the image using **Excel Solver**. All formulas, tables, and steps are included so you can reproduce the solution in Excel.
+
+---
+
+### Problem Statement
+
+Three tasks must be assigned to three machines and all tasks can be done on any machine,
+but with different costs, as described in the scheme below.
+
+<br>
+
+### Problem Recap
+
+- **3 tasks** must be assigned to **3 machines**.
+- Each task can be done by any machine, but with different costs.
+- Each task must be assigned to exactly one machine, and each machine to exactly one task.
+- **Goal:** Minimize total assignment cost.
+
+### Cost Table
+
+|         | Machine 1 | Machine 2 | Machine 3 |
+|---------|-----------|-----------|-----------|
+| Task 1  |     2     |     4     |     3     |
+| Task 2  |     1     |     3     |     2     |
+| Task 3  |     5     |     2     |     4     |
+
+---
+
+## Step 1: Set Up the Excel Spreadsheet
+
+### 1. Enter the Cost Matrix
+
+|     | B    | C    | D    |
+|-----|------|------|------|
+|     | M1   | M2   | M3   |
+| T1  |  2   |  4   |  3   |
+| T2  |  1   |  3   |  2   |
+| T3  |  5   |  2   |  4   |
+
+- Place this table in cells **B2:D4**.
+
+### 2. Create the Decision Variable Table
+
+|     | G    | H    | I    |
+|-----|------|------|------|
+|     | M1   | M2   | M3   |
+| T1  | x11  | x12  | x13  |
+| T2  | x21  | x22  | x23  |
+| T3  | x31  | x32  | x33  |
+
+- Place this table in **G2:I4**.
+- These cells will be filled with 0 or 1 by the Solver (1 = assigned, 0 = not assigned).
+
+### 3. Calculate the Total Cost
+
+In cell **K2**, enter:
+
+```
+
+=SUMPRODUCT(B2:D4, G2:I4)
+
+```
+
+This formula multiplies each assignment by its cost and sums the total.
+
+### 4. Add Row and Column Sums for Constraints
+
+#### Row Sums (Each Task Assigned Once)
+
+- In **J2**: `=SUM(G2:I2)`
+- In **J3**: `=SUM(G3:I3)`
+- In **J4**: `=SUM(G4:I4)`
+
+#### Column Sums (Each Machine Assigned Once)
+
+- In **G5**: `=SUM(G2:G4)`
+- In **H5**: `=SUM(H2:H4)`
+- In **I5**: `=SUM(I2:I4)`
+
+---
+
+## Step 2: Configure Excel Solver
+
+1. **Go to**: Data > Solver
+2. **Set Objective**:  
+   - Set **K2** (total cost) to **Minimize**.
+3. **By Changing Variable Cells**:  
+   - Select **G2:I4**.
+4. **Add Constraints**:
+   - **J2:J4 = 1** (each task assigned once)
+   - **G5:I5 = 1** (each machine assigned once)
+   - **G2:I4 = binary** (only 0 or 1 allowed)
+5. **Choose Solving Method**:  
+   - Use "Simplex LP" or "GRG Nonlinear" (either works for this size).
+6. **Click Solve**.
+
+---
+
+## Step 3: Solution Example
+
+After running Solver, you should get a solution like:
+
+|     | M1 | M2 | M3 | Row Sum |
+|-----|----|----|----|---------|
+| T1  |  1 |  0 |  0 |   1     |
+| T2  |  0 |  0 |  1 |   1     |
+| T3  |  0 |  1 |  0 |   1     |
+|Col Sum| 1|  1 |  1 |         |
+
+- **Task 1 → Machine 1** (cost 2)
+- **Task 2 → Machine 3** (cost 2)
+- **Task 3 → Machine 2** (cost 2)
+
+**Total minimum cost:** 6
+
+---
+
+## Excel Table and Formula Summary
+
+|     | M1   | M2   | M3   | Row Sum |
+|-----|------|------|------|---------|
+| T1  | G2   | H2   | I2   | J2      |
+| T2  | G3   | H3   | I3   | J3      |
+| T3  | G4   | H4   | I4   | J4      |
+|Col Sum|G5 | H5   | I5   |         |
+
+- **Total Cost:** `=SUMPRODUCT(B2:D4, G2:I4)`
+- **Row Sums:** `=SUM(G2:I2)`, etc.
+- **Column Sums:** `=SUM(G2:G4)`, etc.
+
+---
+
+## Result (in English)
+
+**The optimal assignment is:**
+- Task 1 to Machine 1 (cost 2)
+- Task 2 to Machine 3 (cost 2)
+- Task 3 to Machine 2 (cost 2)
+
+**Total minimum cost:** 6
+
+
+