Beginning Algebra With Applications, Chapter 5, Test, Section Test, Problem 28

A company that manufactures toasters has fixed costs of $\$ 1000$ each month. The manufacturing cost per toaster is $\$ 8$. An equation that represents the total cost to manufacture the toasters is $C = 8t + 1000$, where $C$ is the total cost, in dollars and $t$ is the number of toasters manufactured each month.

a. Write the equation in functional notation.

The equation $C=8t+1000$ can be written in functional notation as $f(x) = 8x+1000$

b. Use the equation in part a to graph the equation for values of $t$ between 0 and 500.

Using the equation in part a, we substitute values of $x = \{ 0,100,200,300,340,400,500 \}$


$\begin{equation} \begin{aligned} f(0) =& 8(0) + 1000 = 1000 \\ f(100) =& 8(100) + 1000 = 1800 \\ f(200) =& 8(200) + 1000 = 2600 \\ f(300) =& 8(300) + 1000 = 3400 \\ f(340) =& 8(340) + 1000 = 3720 \\ f(400) =& 8(400) + 1000 = 4200 \\ f(500) =& 8(500) + 1000 = 5000 \end{aligned} \end{equation}$



The ordered pairs are $(0,1000), (100,1800), (200,2600), (300, 3400), (340,3720), (400,4200), (500,5000)$








c. The point $(340,3720)$ is on the graph. Write a sentence that explains the meaning of this ordered pair.

The ordered pair $(340,3720)$ means that if 340 toasters are manufactured, the total cost is $\$ 3,720$.