Example 6 from Algebra and Trigonometry, 4.1 Linear Functions

Writing an Equation for a Linear Cost Function

Suppose Ben starts a company in which he incurs a fixed cost of $1,250 per month for the overhead, which includes his office rent. His production costs are $37.50 per item. Write a linear function $C$ where $C (x)$ is the cost for $x$ items produced in a given month.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The fixed cost is present every month, $1,250. The costs that can vary include the cost to produce each item, which is $37.50. The variable cost, called the marginal cost, is represented by $37.5.$ The cost Ben incurs is the sum of these two costs, represented by $C (x) = 1250 + 37.5 x .$

How did it go?

Solution

Solution