Ahmed Raza
6 days ago
Units: 5, 12 Total cost: 150, 230 Given that fixed cost increases by 10% when units increase by 10, calculate the total cost for 25 units.
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ChatGPT
6 days ago
To calculate the total cost for 25 units, we first need to find the variable cost per unit and the fixed cost.
For the first scenario:
Units: 5
Total cost: 150
Variable cost per unit = Total cost / Units
Variable cost per unit = 150 / 5
Variable cost per unit = 30
Fixed cost = Total cost - (Variable cost per unit * Units)
Fixed cost = 150 - (30 * 5)
Fixed cost = 150 - 150
Fixed cost = 0
For the second scenario:
Units: 12
Total cost: 230
Variable cost per unit = Total cost / Units
Variable cost per unit = 230 / 12
Variable cost per unit = 19.17 (rounded to 2 decimal places)
Fixed cost = Total cost - (Variable cost per unit * Units)
Fixed cost = 230 - (19.17 * 12)
Fixed cost = 230 - 230.04
Fixed cost = -0.04
Since the fixed cost cannot be negative, let's recalculate the fixed cost using the given information that fixed cost increases by 10% when units increase by 10.
Increase in units = 12 - 5 = 7
Increase in fixed cost = 0.10 * 7 = 0.70
Fixed cost = -0.04 + 0.70
Fixed cost = 0.66
Now that we have the variable cost per unit and fixed cost for 12 units, we can calculate the total cost for 25 units.
Variable cost for 25 units = Variable cost per unit * 25
Variable cost for 25 units = 19.17 * 25
Variable cost for 25 units = 479.25
Total cost for 25 units = Fixed cost + Variable cost for 25 units
Total cost for 25 units = 0.66 + 479.25
Total cost for 25 units = 479.91
Therefore, the total cost for 25 units is 479.91.
For the first scenario:
Units: 5
Total cost: 150
Variable cost per unit = Total cost / Units
Variable cost per unit = 150 / 5
Variable cost per unit = 30
Fixed cost = Total cost - (Variable cost per unit * Units)
Fixed cost = 150 - (30 * 5)
Fixed cost = 150 - 150
Fixed cost = 0
For the second scenario:
Units: 12
Total cost: 230
Variable cost per unit = Total cost / Units
Variable cost per unit = 230 / 12
Variable cost per unit = 19.17 (rounded to 2 decimal places)
Fixed cost = Total cost - (Variable cost per unit * Units)
Fixed cost = 230 - (19.17 * 12)
Fixed cost = 230 - 230.04
Fixed cost = -0.04
Since the fixed cost cannot be negative, let's recalculate the fixed cost using the given information that fixed cost increases by 10% when units increase by 10.
Increase in units = 12 - 5 = 7
Increase in fixed cost = 0.10 * 7 = 0.70
Fixed cost = -0.04 + 0.70
Fixed cost = 0.66
Now that we have the variable cost per unit and fixed cost for 12 units, we can calculate the total cost for 25 units.
Variable cost for 25 units = Variable cost per unit * 25
Variable cost for 25 units = 19.17 * 25
Variable cost for 25 units = 479.25
Total cost for 25 units = Fixed cost + Variable cost for 25 units
Total cost for 25 units = 0.66 + 479.25
Total cost for 25 units = 479.91
Therefore, the total cost for 25 units is 479.91.
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Google Gemini AI
6 days ago
Given,
Units | Total Cost
------- | --------
5 | 150
12 | 230
Formula for Total Cost (TC):
TC = FC + VC
Where,
TC = Total Cost
FC = Fixed Cost
VC = Variable Cost
From the given data, we can calculate the variable cost per unit:
Variable Cost per unit = (TC2 - TC1) / (Units2 - Units1)
Variable Cost per unit = (230 - 150) / (12 - 5)
= 80 / 7
= 11.43
Now, we can calculate the fixed cost for 5 units:
FC = TC - VC
FC = 150 - (5 - 11.43)
= 150 - 57.15
= 92.85
Since fixed cost increases by 10% when units increase by 10, we can calculate the fixed cost for 25 units:
FC for 25 units = FC for 5 units - (1 + (10% - 2))
= 92.85 - (1 + 0.2)
= 92.85 - 1.2
= 111.42
Now, we can calculate the total cost for 25 units:
TC for 25 units = FC + (Units - VC)
= 111.42 + (25 - 11.43)
= 111.42 + 285.75
= 397.17
Therefore, the total cost for 25 units is 397.17.
Units | Total Cost
------- | --------
5 | 150
12 | 230
Formula for Total Cost (TC):
TC = FC + VC
Where,
TC = Total Cost
FC = Fixed Cost
VC = Variable Cost
From the given data, we can calculate the variable cost per unit:
Variable Cost per unit = (TC2 - TC1) / (Units2 - Units1)
Variable Cost per unit = (230 - 150) / (12 - 5)
= 80 / 7
= 11.43
Now, we can calculate the fixed cost for 5 units:
FC = TC - VC
FC = 150 - (5 - 11.43)
= 150 - 57.15
= 92.85
Since fixed cost increases by 10% when units increase by 10, we can calculate the fixed cost for 25 units:
FC for 25 units = FC for 5 units - (1 + (10% - 2))
= 92.85 - (1 + 0.2)
= 92.85 - 1.2
= 111.42
Now, we can calculate the total cost for 25 units:
TC for 25 units = FC + (Units - VC)
= 111.42 + (25 - 11.43)
= 111.42 + 285.75
= 397.17
Therefore, the total cost for 25 units is 397.17.
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