The RideEm Bicycles factory can produce 140 bicycles in a day at a total cost of $10,200 and it can produce 160 bicycles in a day at a total cost of $10,900.
What are the company's daily fixed costs?
What is the marginal cost per bicycle?(How do I find this function?)
Thank you.
20 extra bikes cost $700 more to produce. That is $35 per bike. That is the marginal cost.
When producing 140 bikes, the per-bike part of the cost is 140x35 = $4900
The "daily fixed cost" (labor/rent/overhead) is 10,200 -4900 = $5300.
To find the company's daily fixed costs, we need to determine the cost that remains constant regardless of the level of production. We can do this by subtracting the variable costs from the total costs at either production level.
Let's use the information provided:
When the factory produces 140 bicycles, the total cost is $10,200.
When the factory produces 160 bicycles, the total cost is $10,900.
To find the fixed costs, we need to determine the variable costs first. The variable costs are calculated by subtracting the fixed costs from the total costs.
Variable costs at 140 bicycles production level: $10,200 - Variable costs = $10,200 - Fixed costs
Variable costs at 160 bicycles production level: $10,900 - Variable costs = $10,900 - Fixed costs
Now we can set up an equation to solve for the fixed costs:
10,900 - Variable costs = 10,200 - Fixed costs
Simplifying the equation, we get:
700 = Variable costs - Fixed costs
Since the variable costs change with the level of production, we subtract the variable costs of producing 140 bicycles from the variable costs of producing 160 bicycles:
700 = (Variable costs at 160 bicycles) - (Variable costs at 140 bicycles)
Substituting the given information:
700 = (10,900 - Fixed costs) - (10,200 - Fixed costs)
Simplifying further:
700 = 10,900 - Fixed costs - 10,200 + Fixed costs
Now we can cancel out the Fixed costs terms:
700 = 700
This equation is true, indicating that we made no errors. Therefore, the fixed costs are $700.
To find the marginal cost per bicycle, we need to calculate the change in total costs when the production level increases by one bicycle.
Marginal cost can be calculated by taking the difference in total costs and dividing it by the change in the quantity of bicycles produced.
Marginal cost per bicycle = (Total cost at 160 bicycles – Total cost at 140 bicycles) / (160 – 140)
Marginal cost per bicycle = ($10,900 - $10,200) / (160 - 140)
Marginal cost per bicycle = $700 / 20
Marginal cost per bicycle = $35
Therefore, the company's daily fixed costs are $700 and the marginal cost per bicycle is $35.
To find the daily fixed costs of the RideEm Bicycles factory, we need to determine the portion of the total cost that remains constant regardless of the number of bicycles produced. The fixed costs do not change with the level of production.
To find the fixed costs, we can use the information provided in both scenarios. Let's denote the fixed costs as "FC."
We are given two sets of information:
- In the first scenario, the factory produces 140 bicycles at a total cost of $10,200.
- In the second scenario, the factory produces 160 bicycles at a total cost of $10,900.
Let's set up two equations based on the given information:
Equation 1: FC + (Unit Cost * Quantity 1) = Total Cost 1
Equation 2: FC + (Unit Cost * Quantity 2) = Total Cost 2
In Equation 1, the quantity is 140 bicycles and the total cost is $10,200. We don't know the unit cost yet, so we can represent it as "UC."
FC + (UC * 140) = $10,200
In Equation 2, the quantity is 160 bicycles and the total cost is $10,900.
FC + (UC * 160) = $10,900
Now we have a system of two equations with two variables (FC and UC). We can solve for FC by subtracting one equation from the other:
(FC + (UC * 160)) - (FC + (UC * 140)) = $10,900 - $10,200
UC * 160 - UC * 140 = $10,900 - $10,200
UC * (160 - 140) = $10,900 - $10,200
UC * 20 = $700
UC = $700 / 20
UC = $35
Now that we have the unit cost, we can substitute it back into one of the original equations to find the fixed costs (FC):
FC + ($35 * 140) = $10,200
FC + $4,900 = $10,200
FC = $10,200 - $4,900
FC = $5,300
Therefore, the daily fixed costs of the RideEm Bicycles factory are $5,300.
Now let's move on to finding the marginal cost per bicycle. The marginal cost represents the additional cost incurred when producing one additional bicycle. In other words, it is the change in total cost divided by the change in quantity.
To find the marginal cost per bicycle, we need to calculate the unit cost for each scenario:
In the first scenario:
FC + (UC * 140) = $10,200
$5,300 + (UC * 140) = $10,200
UC * 140 = $10,200 - $5,300
UC * 140 = $4,900
UC = $4,900 / 140
UC = $35
In the second scenario:
FC + (UC * 160) = $10,900
$5,300 + (UC * 160) = $10,900
UC * 160 = $10,900 - $5,300
UC * 160 = $5,600
UC = $5,600 / 160
UC = $35
As you can see, the unit cost (UC) remains the same in both scenarios. This means that the marginal cost per bicycle is equal to the unit cost, which is $35.
Hence, the answer to your question is that the company's daily fixed costs are $5,300, and the marginal cost per bicycle is $35.