QuestionRideEm Bicycles produces 170 bikes for \C(x)$ and fixed/variable costs.
Studdy Solution
STEP 1
Assumptions1. The relationship between the number of bicycles produced and the total cost is linear.
. The total cost consists of fixed costs and variable costs.
3. The fixed costs are the same regardless of the number of bicycles produced.
4. The variable costs change with the number of bicycles produced.
STEP 2
First, we need to find the slope of the line that represents the relationship between the number of bicycles and the total cost. The slope is the change in cost divided by the change in the number of bicycles.
STEP 3
Now, plug in the given values for the change in cost and the change in the number of bicycles to calculate the slope.
STEP 4
Calculate the slope.
STEP 5
The slope represents the variable cost per bicycle, which is \$30.
STEP 6
Now, we can find the fixed costs by plugging in the values for the cost, the number of bicycles, and the variable cost per bicycle into the equation for a line, , where is the cost, is the slope (variable cost per bicycle), is the number of bicycles, and is the y-intercept (fixed costs).
STEP 7
Rearrange the equation to solve for the fixed costs.
STEP 8
Plug in the values for the cost, the number of bicycles, and the variable cost per bicycle to calculate the fixed costs.
STEP 9
Calculate the fixed costs.
The fixed costs are \$5,200.
STEP 10
The linear function that models the total cost for RideEm to produce bicycles isRideEm's daily fixed costs are \$5,200 and the variable costs are \$30 per bicycle.
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