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FASE 1 (Toma de decisiones bajo riesgo).
Desarrolla a mano en una hoja de papel la solución del problema, utilizando el método de toma 
de decisiones bajo riesgo; para conocer la alternativa de decisión que minimizará el costo de 
la venta de software.
a) Resuelve las alternativas de decisión.
b) Calcula el valor esperado de la empresa.
c) Muestra con rojo la decisión que minimizará el costo de la venta de software.


To solve this problem using the **decision-making under risk** method, we'll need to evaluate the expected cost for each alternative and then choose the one that minimizes the expected cost. Here’s a step-by-step outline of how to proceed with the information provided:

### Step 1: Define the decision alternatives and probabilities
The company has three decision alternatives:
1. **Development of e-commerce platforms**
2. **Inventory management systems**
3. **Payroll software**

The potential demand levels and their associated probabilities are:
- **High demand (0.43)**
- **Medium demand (0.36)**
- **Low demand (0.21)**

### Step 2: Cost table
Based on the given data, the costs for each decision alternative are:

| Alternatives                            | High Demand (0.43) | Medium Demand (0.36) | Low Demand (0.21) |
|-----------------------------------------|--------------------|----------------------|-------------------|
| **Development of e-commerce platforms** | 75,000             | 70,000               | 65,000            |
| **Inventory management systems**        | 85,000             | 80,000               | 70,000            |
| **Payroll software**                    | 70,000             | 65,000               | 50,000            |

### Step 3: Calculate the expected cost for each alternative
The expected cost for each alternative is computed as the sum of the products of each demand level's cost and its probability:

\[
\text{Expected Cost} = P(\text{High}) \times \text{Cost(High)} + P(\text{Medium}) \times \text{Cost(Medium)} + P(\text{Low}) \times \text{Cost(Low)}
\]

**For Development of e-commerce platforms**:
\[
\text{Expected Cost} = (0.43 \times 75,000) + (0.36 \times 70,000) + (0.21 \times 65,000)
\]
\[
\text{Expected Cost} = 32,250 + 25,200 + 13,650 = 71,100
\]

**For Inventory management systems**:
\[
\text{Expected Cost} = (0.43 \times 85,000) + (0.36 \times 80,000) + (0.21 \times 70,000)
\]
\[
\text{Expected Cost} = 36,550 + 28,800 + 14,700 = 80,050
\]

**For Payroll software**:
\[
\text{Expected Cost} = (0.43 \times 70,000) + (0.36 \times 65,000) + (0.21 \times 50,000)
\]
\[
\text{Expected Cost} = 30,100 + 23,400 + 10,500 = 64,000
\]

### Step 4: Highlight the best decision
The **Payroll software** alternative has the lowest expected cost of **64,000**. Therefore, this is the best option to minimize the cost of software sales.

---

### Final Decision
- The decision that minimizes the cost is the **Payroll software** option, with an expected cost of **64,000** pesos (highlighted in red in your handwritten solution).

### Tip:
When solving decision-making problems under risk, always multiply each outcome's cost by the corresponding probability, then sum these products to get the expected value.

---

Let me know if you would like a detailed explanation on any step. Here are five related questions for further exploration:

1. What are the main differences between decision-making under risk and uncertainty?
2. How would changes in demand probabilities affect the expected costs?
3. Could a sensitivity analysis help in this type of decision-making?
4. How would a decision tree visualize the current problem?
5. How does decision-making under risk differ from decision-making under certainty?

Tip: In decision-making problems, always verify the probabilities sum up to 1 to ensure consistency in the model.

FASE 1 (Toma de decisiones bajo riesgo). Desarrolla a mano en una hoja de papel la solución del problema, utilizando el método de toma de decisiones bajo riesgo; para conocer la alternativa de decisión que minimizará el costo de la venta de software. a) Resuelve las alternativas de decisión. b) Calcula el valor esperado de la empresa. c) Muestra con rojo la decisión que minimizará el costo de la venta de software.

Learn how to solve a decision-making problem under risk to minimize the cost of software sales. This problem involves calculating the expected cost for different alternatives using probability, with solutions and steps provided.

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