A company manufactures high-end racing bicycles. The total cost to manufacture 25 bikes is $21950. The
daily fixed costs are $2075. Fixed costs refers to expenses that must be paid even when producing zero
bikes, such as rent, utilities, etc. Assume that total cost, C, is linearly related to the number of bicycles, x,
that the company manufactures
To determine the variable cost per bike, we need to find the slope of the linear equation relating the total cost to the number of bicycles manufactured. We can then subtract the fixed costs from the total cost to find the variable cost.
Given:
Total cost to manufacture 25 bikes = $21950
Daily fixed costs = $2075
Let's set up the equation:
C = mx + b
Where:
C = Total cost
m = Slope (variable cost per bike)
x = Number of bicycles manufactured
b = y-intercept (fixed costs)
We are given that the total cost to manufacture 25 bikes is $21950. Plugging this into the equation, we have:
21950 = m * 25 + 2075
Now, we can solve for m (the slope):
Subtract 2075 from both sides of the equation:
21950 - 2075 = m * 25
19875 = m * 25
Divide both sides of the equation by 25:
m = 19875 / 25
m = 795
So, the slope (variable cost per bike) is $795.
To find the variable cost per bike, we subtract the fixed costs from the total cost per bike:
Variable cost per bike = Total cost per bike - Fixed costs
Variable cost per bike = 795 - 2075
Variable cost per bike = -$1280
The negative sign indicates that the manufacturing cost per bike is less than the fixed costs. Therefore, the variable cost per bike is -$1280. This suggests that the company is either making a loss per bike or there may be an error in the given information.