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Sagot :
To determine the crashing cost per day for each activity in the project, we need to follow these steps:
1. Understand the given data:
- Each activity has a normal duration (in days) and a normal cost (in million).
- Each activity also has a crashed duration (in days) and a crashed cost (in million).
- Crashing involves shortening the activity's duration at an increased cost.
2. Calculate the crashing cost per day:
- For each activity that can be crashed, compute the crashing cost per day using the formula:
[tex]\[ \text{Crashing cost per day} = \frac{\text{Crashed cost} - \text{Normal cost}}{\text{Normal duration} - \text{Crashed duration}} \][/tex]
3. Apply the formula to each activity and determine the crashing costs.
### Given Data and Calculation:
1. Activity A:
- Normal duration: 5 days
- Normal cost: 100 million
- Crashed duration: 3 days
- Crashed cost: 1500 million
[tex]\[ \text{Crashing cost per day for A} = \frac{1500 - 100}{5 - 3} = \frac{1400}{2} = 700 \text{ million per day} \][/tex]
2. Activity B:
- Normal duration: 7 days
- Normal cost: 700 million
- Crashed duration: 6 days
- Crashed cost: 0 million (not given, assume it is 0 for calculation)
[tex]\[ \text{Crashing cost per day for B} = \frac{0 - 700}{7 - 6} = \frac{-700}{1} = -700 \text{ million per day} \][/tex]
3. Activity C:
- Normal duration: 3 days
- Normal cost: 0 million (not given, assume it is 0 for calculation)
- Crashed duration: None (not given, assume it is same as normal duration)
[tex]\[ \text{Crashing cost per day for C} = 0 \text{ million per day} \][/tex]
4. Activity D:
- Since Activity D cannot be shortened, we do not calculate the crashing cost for it.
5. Activity E:
- Normal duration: 9 days
- Normal cost: 3750 million
- Crashed duration: 6 days
- Crashed cost: 9000 million
[tex]\[ \text{Crashing cost per day for E} = \frac{9000 - 3750}{9 - 6} = \frac{5250}{3} = 1750 \text{ million per day} \][/tex]
6. Activity F:
- Normal duration: 4 days
- Normal cost: 0 million (not given, assume it is 0 for calculation)
- Crashed duration: None (not given, assume it is same as normal duration)
[tex]\[ \text{Crashing cost per day for F} = 0 \text{ million per day} \][/tex]
7. Activity G:
- Normal duration: None (not given, assume it is same as crashed duration)
- Normal cost: 1600 million
- Crashed duration: 3 days
- Crashed cost: 2500 million
[tex]\[ \text{Crashing cost per day for G} = 0 \text{ million per day} \][/tex]
8. Activity H:
- Normal duration: 8 days
- Normal cost: 9000 million
- Crashed duration: 5 days
- Crashed cost: 15000 million
[tex]\[ \text{Crashing cost per day for H} = \frac{15000 - 9000}{8 - 5} = \frac{6000}{3} = 2000 \text{ million per day} \][/tex]
### Summary of Crashing Costs per Day for Each Activity:
- Activity A: 700 million per day
- Activity B: -700 million per day
- Activity C: 0 million per day
- Activity D: Not applicable (cannot be shortened)
- Activity E: 1750 million per day
- Activity F: 0 million per day
- Activity G: 0 million per day
- Activity H: 2000 million per day
Thus, these are the crashing costs for each activity in the project.
1. Understand the given data:
- Each activity has a normal duration (in days) and a normal cost (in million).
- Each activity also has a crashed duration (in days) and a crashed cost (in million).
- Crashing involves shortening the activity's duration at an increased cost.
2. Calculate the crashing cost per day:
- For each activity that can be crashed, compute the crashing cost per day using the formula:
[tex]\[ \text{Crashing cost per day} = \frac{\text{Crashed cost} - \text{Normal cost}}{\text{Normal duration} - \text{Crashed duration}} \][/tex]
3. Apply the formula to each activity and determine the crashing costs.
### Given Data and Calculation:
1. Activity A:
- Normal duration: 5 days
- Normal cost: 100 million
- Crashed duration: 3 days
- Crashed cost: 1500 million
[tex]\[ \text{Crashing cost per day for A} = \frac{1500 - 100}{5 - 3} = \frac{1400}{2} = 700 \text{ million per day} \][/tex]
2. Activity B:
- Normal duration: 7 days
- Normal cost: 700 million
- Crashed duration: 6 days
- Crashed cost: 0 million (not given, assume it is 0 for calculation)
[tex]\[ \text{Crashing cost per day for B} = \frac{0 - 700}{7 - 6} = \frac{-700}{1} = -700 \text{ million per day} \][/tex]
3. Activity C:
- Normal duration: 3 days
- Normal cost: 0 million (not given, assume it is 0 for calculation)
- Crashed duration: None (not given, assume it is same as normal duration)
[tex]\[ \text{Crashing cost per day for C} = 0 \text{ million per day} \][/tex]
4. Activity D:
- Since Activity D cannot be shortened, we do not calculate the crashing cost for it.
5. Activity E:
- Normal duration: 9 days
- Normal cost: 3750 million
- Crashed duration: 6 days
- Crashed cost: 9000 million
[tex]\[ \text{Crashing cost per day for E} = \frac{9000 - 3750}{9 - 6} = \frac{5250}{3} = 1750 \text{ million per day} \][/tex]
6. Activity F:
- Normal duration: 4 days
- Normal cost: 0 million (not given, assume it is 0 for calculation)
- Crashed duration: None (not given, assume it is same as normal duration)
[tex]\[ \text{Crashing cost per day for F} = 0 \text{ million per day} \][/tex]
7. Activity G:
- Normal duration: None (not given, assume it is same as crashed duration)
- Normal cost: 1600 million
- Crashed duration: 3 days
- Crashed cost: 2500 million
[tex]\[ \text{Crashing cost per day for G} = 0 \text{ million per day} \][/tex]
8. Activity H:
- Normal duration: 8 days
- Normal cost: 9000 million
- Crashed duration: 5 days
- Crashed cost: 15000 million
[tex]\[ \text{Crashing cost per day for H} = \frac{15000 - 9000}{8 - 5} = \frac{6000}{3} = 2000 \text{ million per day} \][/tex]
### Summary of Crashing Costs per Day for Each Activity:
- Activity A: 700 million per day
- Activity B: -700 million per day
- Activity C: 0 million per day
- Activity D: Not applicable (cannot be shortened)
- Activity E: 1750 million per day
- Activity F: 0 million per day
- Activity G: 0 million per day
- Activity H: 2000 million per day
Thus, these are the crashing costs for each activity in the project.
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