The RideEm bicycles factory can produce 100 bicycles in a day at a total cost of $10,100, and it can produce 120 bicycles in a day at a total cost of $10,700.
A)Find a linear function that models the total cost for RideEm to produce x bicycles
B) what are the companies daily fixed costs and variable costs?
c = a n + b
10100 = 100 a + b
10700 = 120 a + b
=====================subtract
-600 = -20 a
a = 30 etc. go back and get b
-600 = -20 a
To find a linear function that models the total cost for RideEm to produce x bicycles, we need to determine the relation between the number of bicycles produced and the total cost.
Let's denote the number of bicycles produced as x and the total cost as C.
We are given two data points:
When x = 100, C = 10100
When x = 120, C = 10700
To find the equation for the linear function, we need to find the slope (m) and the y-intercept (b).
Using the point-slope formula: (C - C1) / (x - x1) = m
Let's use the values from the first data point: (100, 10100)
(C - 10100) / (x - 100) = m
m = (C - 10100) / (x - 100)
Now, we can substitute the values from the second data point: (120, 10700)
m = (10700 - 10100) / (120 - 100)
m = 600 / 20
m = 30
Now, we have the value of m. Let's find the y-intercept.
Using the equation: C = mx + b, where m = 30 (slope) and (x, C) is any point on the line.
10100 = 30(100) + b
10100 = 3000 + b
b = 10100 - 3000
b = 7100
Therefore, the linear function that models the total cost for RideEm to produce x bicycles is:
C = 30x + 7100
Now, let's determine the company's daily fixed costs and variable costs.
The fixed costs represent the costs that do not change with the number of bicycles produced. In this case, the fixed costs can be calculated by substituting x = 0 into the linear function:
C = 30(0) + 7100
C = 7100
Therefore, the daily fixed costs for RideEm are $7100.
The variable costs represent the costs that change with the number of bicycles produced. In this case, the variable costs can be calculated by subtracting the fixed costs from the total cost:
Variable costs = Total costs - Fixed costs
Variable costs = C - 7100
Note that for this specific problem, without additional information, we cannot determine the exact variable costs as it will vary depending on the number of bicycles produced.
To find a linear function that models the total cost for RideEm to produce x bicycles, we can use the information given in the problem.
Let's first define some variables:
- Let C represent the total cost.
- Let x represent the number of bicycles produced.
We have two data points with their respective costs: (100, $10,100) and (120, $10,700).
A) To find the linear function, we need to find the slope and the y-intercept of the line.
1. Let's find the slope (m):
We use the formula for slope, which is given by:
m = (y2 - y1) / (x2 - x1)
m = ($10,700 - $10,100) / (120 - 100)
= $600 / 20
= $30
So, the slope of the linear function is 30.
2. Let's find the y-intercept (b):
We can use the point-slope form of a line, which is given by:
y - y1 = m(x - x1)
Using one of the points (100, $10,100):
10,100 - y1 = 30(100 - x1)
10,100 - y1 = 3000 - 30x1
y1 = 30x1 + 7100
Therefore, the y-intercept (b) is 7100.
Hence, the linear function that models the total cost (C) for RideEm to produce x bicycles is:
C = 30x + 7100.
B) Now, let's determine the company's daily fixed costs and variable costs.
The linear function can be divided into two parts:
1. Fixed costs: These costs remain constant regardless of the number of bicycles produced. In our case, the fixed costs are represented by the y-intercept (b). So, the daily fixed costs for RideEm are $7100.
2. Variable costs: These costs change as the number of bicycles produced changes. In our case, the variable costs are represented by the slope (m). So, the variable cost per bicycle produced by RideEm is $30.
Therefore, the company's daily fixed costs are $7100, and the variable costs per bicycle produced are $30.