Question 4 [18 marks]
The University of the Free State (UFS) has decided to purchase two brand new 65-seater buses. As leading automotive business consultants, the UFS fleet manager has approached your team for advice on the most suitable buses that meet their needs in the market. Four quotations have been submitted to your team. Make use of the weighted average method to select the best two buses that should be purchased.
The criteria for selecting the buses are as follows:
▪ Price: 10
▪ Fuel efficiency: 9
▪ Comfort: 7
▪ Durability: 10
▪ After-sales service: 8
▪ Handling: 6
POINTS
Tata
Mercedes Benz
Volkswagen
Toyota
Price
10
6
7
8
Fuel efficiency
10
8
8
9
Comfort
6
8
8
9
Durability
5
7
9
8
After-sales service
10
9
7
7
Handling
6
8
9
7
Make use of the weighted average method to select the best three (3) buses that should be purchased.
4.1 Use the weighted average method to select the best three (3) buses that you advise the UFS to purchase (use a tabular presentation).
[16]
4.2 Indicate which three (3) buses are best for the purchase and motivate your answer.
4.1: Tabular Presentation
Criteria Tata Mercedes Benz Volkswagen Toyota
Price 10 6 7 8
Fuel efficiency 10 8 8 9
Comfort 6 8 8 9
Durability 5 7 9 8
After-sales service 10 9 7 7
Handling 6 8 9 7
To calculate the weighted average for each bus, we multiply the score for each criterion by its weight, and then sum up the values.
Criteria Tata Mercedes Benz Volkswagen Toyota
Price 10*10=100 6*10=60 7*10=70 8*10=80
Fuel efficiency 10*9=90 8*9=72 8*9=72 9*9=81
Comfort 6*7=42 8*7=56 8*7=56 9*7=63
Durability 5*10=50 7*10=70 9*10=90 8*10=80
After-sales service 10*8=80 9*8=72 7*8=56 7*8=56
Handling 6*6=36 8*6=48 9*6=54 7*6=42
Total Score 318 358 398 402
Therefore, the top three buses that should be purchased according to the weighted average method are:
1. Toyota with a total score of 402
2. Volkswagen with a total score of 398
3. Mercedes Benz with a total score of 358
4.2: Motivation for the selected buses:
1. Toyota: It has the highest total score, indicating that it performs well in all criteria. It has high scores in fuel efficiency, comfort, durability, and after-sales service.
2. Volkswagen: It has the second-highest total score, showing good performance in most criteria. It has high scores in fuel efficiency, comfort, durability, and handling.
3. Mercedes Benz: While it has the lowest total score among the selected buses, it still performs well in most criteria. It has high scores in fuel efficiency, comfort, durability, and after-sales service.
Overall, these three buses are the best choices based on their performance in the weighted average method, considering the criteria of price, fuel efficiency, comfort, durability, after-sales service, and handling.
4.1 To determine the best three buses using the weighted average method, we need to assign weights to each criterion and calculate the weighted average for each bus.
Using the weights provided in the question (Price: 10, Fuel efficiency: 9, Comfort: 7, Durability: 10, After-sales service: 8, Handling: 6), we can calculate the weighted average for each bus as follows:
Tata:
Weighted average = (Price * 10 + Fuel efficiency * 10 + Comfort * 6 + Durability * 5 + After-sales service * 10 + Handling * 6) / (10 + 9 + 7 + 10 + 8 + 6)
= (10 * 10 + 10 * 10 + 6 * 6 + 5 * 5 + 10 * 10 + 6 * 6) / 50
= (100 + 100 + 36 + 25 + 100 + 36) / 50
= 397 / 50
= 7.94
Mercedes Benz:
Weighted average = (Price * 6 + Fuel efficiency * 8 + Comfort * 8 + Durability * 7 + After-sales service * 9 + Handling * 8) / (10 + 9 + 7 + 10 + 8 + 6)
= (6 * 6 + 8 * 8 + 8 * 6 + 7 * 7 + 9 * 10 + 8 * 6) / 50
= (36 + 64 + 48 + 49 + 90 + 48) / 50
= 335 / 50
= 6.7
Volkswagen:
Weighted average = (Price * 7 + Fuel efficiency * 8 + Comfort * 8 + Durability * 9 + After-sales service * 7 + Handling * 9) / (10 + 9 + 7 + 10 + 8 + 6)
= (7 * 7 + 8 * 8 + 8 * 7 + 9 * 9 + 7 * 10 + 9 * 6) / 50
= (49 + 64 + 56 + 81 + 70 + 54) / 50
= 374 / 50
= 7.48
Toyota:
Weighted average = (Price * 8 + Fuel efficiency * 9 + Comfort * 9 + Durability * 8 + After-sales service * 7 + Handling * 7) / (10 + 9 + 7 + 10 + 8 + 6)
= (8 * 8 + 9 * 9 + 9 * 7 + 8 * 8 + 7 * 10 + 7 * 6) / 50
= (64 + 81 + 63 + 64 + 70 + 42) / 50
= 384 / 50
= 7.68
Now, let's summarize the results in a table:
| Bus | Weighted Average |
|---------|-----------------|
| Tata | 7.94 |
|Mercedes | 6.7 |
|Volkswagen| 7.48 |
| Toyota | 7.68 |
4.2 Based on the weighted average calculations, the three best buses for purchase are Tata, Volkswagen, and Toyota. These buses have the highest weighted averages compared to the Mercedes Benz. The Tata bus has the highest weighted average of 7.94, followed by Toyota with 7.68, and Volkswagen with 7.48. Therefore, these three buses are the most suitable choices for the UFS fleet manager to purchase as they meet the criteria of price, fuel efficiency, comfort, durability, after-sales service, and handling to the greatest extent.
To determine the best three buses to advise the University of the Free State (UFS) to purchase, we will use the weighted average method. This method involves assigning weights to each criterion based on their importance and then calculating the weighted average for each bus.
First, let's assign weights to each criterion based on their importance:
- Price: 10
- Fuel efficiency: 9
- Comfort: 7
- Durability: 10
- After-sales service: 8
- Handling: 6
The weights should be scaled such that the total sum of all weights equals 100.
Now, we need to calculate the weighted average for each bus using the given criteria and weights. We will create a table to organize the information:
| Criteria | Tata | Mercedes Benz | Volkswagen | Toyota |
|---------------------|--------|---------------|------------|--------|
| Price | 10 | 6 | 7 | 8 |
| Fuel efficiency | 10 | 8 | 8 | 9 |
| Comfort | 6 | 8 | 8 | 9 |
| Durability | 5 | 7 | 9 | 8 |
| After-sales service | 10 | 9 | 7 | 7 |
| Handling | 6 | 8 | 9 | 7 |
To calculate the weighted average for each bus, we multiply the score for each criterion by its weight and sum them up. Let's perform the calculations:
For Tata:
Weighted Average = (10 * 10) + (10 * 9) + (6 * 7) + (5 * 10) + (10 * 8) + (6 * 6) = 236
For Mercedes Benz:
Weighted Average = (6 * 10) + (8 * 9) + (8 * 7) + (7 * 10) + (9 * 8) + (8 * 6) = 276
For Volkswagen:
Weighted Average = (7 * 10) + (8 * 9) + (8 * 7) + (9 * 10) + (7 * 8) + (9 * 6) = 279
For Toyota:
Weighted Average = (8 * 10) + (9 * 9) + (9 * 7) + (8 * 10) + (7 * 8) + (7 * 6) = 275
Now, let's rank the buses based on their weighted averages in descending order:
1. Volkswagen - Weighted Average: 279
2. Toyota - Weighted Average: 275
3. Mercedes Benz - Weighted Average: 276
4. Tata - Weighted Average: 236
Based on the weighted average method, the three buses with the highest scores are Volkswagen, Toyota, and Mercedes Benz. These are the buses that I would advise the UFS to purchase.
The weighted average method takes into account the importance of different criteria and provides an overall score for each option. In this case, Volkswagen scored the highest weighted average, indicating it performs well across multiple criteria. Toyota and Mercedes Benz also scored well, making them suitable choices for purchase.