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2.2	Una empresa productora de papel quiere determinar la productividad de sus dos plantas industriales, una ubicada en Trujillo y otra en Chiclayo. Los datos con los que se cuenta son los siguientes:


a)	Calcular la productividad de un solo factor mano de obra, materia prima y energía.  Para ambas plantas y comente los resultados.
b)	Calcular la productividad de factores múltiples para ambas plantas y comente los resultados. 



Let's start by extracting the relevant data from the image to solve the given problems.

### Data from the Image

| **Parameter**                     | **Planta Trujillo** | **Planta Chiclayo** |
|-----------------------------------|---------------------|---------------------|
| Número empleados                  | 150                 | 180                 |
| Número horas empleado             | 8 diarias           | 9 diarias           |
| Costo mano de obra                | 10 S/. / hora       | 5 S/. / hora        |
| Materia prima principal           | 5 kg / kg papel     | 5 kg / kg papel     |
| Costo materia prima               | 2 S/. / kg papel    | 1.5 S/. / kg papel  |
| Energía                           | 0.5 Kw / kg papel   | 0.5 Kw / kg papel   |
| Costo energía                     | 1 S/. / Kw          | 1.2 S/. / Kw        |
| Producción diaria                 | 3 TM                | 2.8 TM              |
| Precio Venta                      | 400 S/. / TM        | 400 S/. / TM        |

### Step-by-Step Calculations

#### a) Productividad de un solo factor (mano de obra, materia prima, energía)

1. **Productividad de mano de obra (Labor Productivity):**
   \[
   \text{Productividad de mano de obra} = \frac{\text{Producción diaria}}{\text{Número de empleados} \times \text{Horas diarias}}
   \]

2. **Productividad de materia prima (Material Productivity):**
   \[
   \text{Productividad de materia prima} = \frac{\text{Producción diaria}}{\text{Cantidad de materia prima utilizada}}
   \]

3. **Productividad de energía (Energy Productivity):**
   \[
   \text{Productividad de energía} = \frac{\text{Producción diaria}}{\text{Cantidad de energía utilizada}}
   \]

#### b) Productividad de factores múltiples (MFP)

\[
\text{Productividad de factores múltiples (MFP)} = \frac{\text{Valor de la producción (Ingreso Total)}}{\text{Costo total de los insumos (mano de obra + materia prima + energía)}}
\]

Let's perform the necessary calculations.### Results

#### a) Productividad de un solo factor

1. **Mano de obra (Labor Productivity):**
   - **Trujillo:** 2.5 kg de papel por hora de trabajo
   - **Chiclayo:** 1.73 kg de papel por hora de trabajo

2. **Materia prima (Material Productivity):**
   - **Trujillo:** 0.2 kg de papel por kg de materia prima
   - **Chiclayo:** 0.2 kg de papel por kg de materia prima

3. **Energía (Energy Productivity):**
   - **Trujillo:** 2 kg de papel por kW de energía
   - **Chiclayo:** 2 kg de papel por kW de energía

#### b) Productividad de factores múltiples (MFP)

- **Trujillo:** 0.0276
- **Chiclayo:** 0.0364

### Commentary on Results

1. **Labor Productivity:** The Trujillo plant has higher labor productivity compared to the Chiclayo plant (2.5 vs. 1.73). This indicates that the Trujillo plant is producing more paper per hour of work, which could be due to better processes, less downtime, or more skilled workers.

2. **Material Productivity:** Both plants have the same material productivity (0.2), meaning they use the same amount of material to produce a unit of paper.

3. **Energy Productivity:** Both plants are also equally efficient in terms of energy use, producing 2 kg of paper per kW of energy consumed.

4. **Multiple Factor Productivity (MFP):** The Chiclayo plant has a higher MFP (0.0364) than the Trujillo plant (0.0276). This suggests that the Chiclayo plant is more efficient when considering all inputs (labor, material, and energy) together, despite its lower labor productivity. The lower cost of labor and raw materials in Chiclayo contributes to its overall higher productivity.

Would you like more details or have any specific questions?

### Related Questions to Explore

1. How does the cost of labor impact overall productivity in both plants?
2. What measures could be taken to improve labor productivity in the Chiclayo plant?
3. How does energy cost efficiency differ between the two plants?
4. What strategies could be implemented to reduce material costs in both plants?
5. How could improvements in one input (e.g., labor, material) affect the overall multiple factor productivity?

### Tip

To improve overall productivity, focus on reducing waste and optimizing the most costly inputs, such as labor or materials, while maintaining or improving the output level.

Explore how to calculate productivity in a paper production company's plants in Trujillo and Chiclayo. Learn about labor, material, and energy productivity factors. Detailed calculations and analysis provided.

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