MAT 140 Video Lesson 1: linear equations, revenue, cost, profit Suppose a Kindel manufacturer has the total cost function \( C(x)=130 x+21500 \) and the total revenue function \( R(x)=325 x \) where \( x \) is the number of Kindels. a. Find \( C(20) \) and write a sentence that explains its meaning.

To find \( C(20) \), substitute \( x = 20 \) into the cost function: \[ C(20) = 130(20) + 21500 = 2600 + 21500 = 24100. \] This means that the total cost of manufacturing 20 Kindels is $24,100. When manufacturers analyze costs, it helps them understand how much money they'll need to produce a certain number of products. Knowing the cost for producing a specific quantity can guide pricing strategies and overall financial planning! To truly sharpen your understanding, consider looking into how businesses calculate break-even points. This will show you when total revenue equals total costs, indicating when a company starts making a profit. It's a vital concept for any budding entrepreneur!