A company manufactures high-end racing bicycles. The total cost to manufacture 28 bikes is $25005. The daily fixed costs are $2605. 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.
The cost function is:
C = 2605 + (25005/28)x
To find the cost function, we need to determine the relationship between the number of bicycles produced (x) and the total cost (C). Given that the cost function is assumed to be linear, we can use the equation of a straight line, which can be written as:
C = mx + b
Where:
C is the total cost
m is the slope of the line
x is the number of bicycles produced
b is the y-intercept (constant term)
To determine the cost function, we need to find the values of m and b. We have some information given in the problem:
Number of bicycles produced (x): 28
Total cost to manufacture 28 bikes: $25005
From this information, we can substitute the values into the equation and solve for the constants:
25005 = 28m + b
We also have the information about the daily fixed costs:
Daily fixed costs (b): $2605
Substituting this value into the equation, we get:
25005 = 28m + 2605
Solving for m, we can rearrange the equation:
28m = 25005 - 2605
28m = 22400
m = 800
Now that we have the value of m, we can substitute it back into the equation to solve for b:
25005 = 28 * 800 + b
25005 = 22400 + b
Solving for b:
b = 25005 - 22400
b = 2605
Now we have the values for m and b, which allows us to write the cost function:
C = 800x + 2605
So, the cost function for manufacturing high-end racing bicycles is C = 800x + 2605.