Question

The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To define a formula for the total cost, we need to know two things. The first is the manufacturer's fixed costs. This amount covers expenses such as plant maintenance and insurance, and it is the same no matter how many items are produced. The second thing we need to know is the cost for each unit produced, which is called the variable cost.

Assume that a manufacturer of widgets has fixed costs of $1500 per month and that the variable cost is $20 per widget (so it costs $20 to produce 1 widget).

Yet another widget manufacturer has defined the following: The total cost is $2700 when 100 widgets are produced in a month, and the total cost is $3500 when 150 widgets are produced in a month. What are the fixed costs and variable costs for this manufacturer?

Answer 1

To determine the fixed costs and variable costs, set up a system of equations using total cost values at specific production levels, then solve for the variable cost and fixed costs.

Step-by-step explanation:

The student has asked how to determine the fixed costs and variable costs for a widget manufacturer given two total cost values at specific production levels. We can solve this by setting up a system of equations based on the formula for total cost, C = fixed costs + (variable cost per unit × number of units produced). With the information that the total cost is $2700 for 100 widgets and $3500 for 150 widgets, we can set up the following equations:

1. Fixed Costs + (Variable Cost × 100) = $2700

2. Fixed Costs + (Variable Cost × 150) = $3500

Subtracting the first equation from the second gives:

(Variable Cost × 50) = $800

From which we can find the variable cost per widget.

Then, substituting the variable cost back into any of the equations will give us the fixed costs.