The cost function for a certain model of a digital camera given by $C = 13.50 x + 48,950$, where $C$ is the cost (in dollars) and $x$ is the number of cameras produced. Find the average cost per unit when $x = 200$. Round your answer to the nearest cent.
A) $\$ 51,650.00$
B) $\$ 244.75$
C) $\$ 13.50$
D) $\$ 258.25$
E) $\$ 244.82$

Question

Quizplus · Accepted Answer

The average cost per unit is given by the total cost divided by the number of units produced:

$$\text{Average cost per unit} = \frac{\text{Total cost}}{\text{Number of units produced}}$$

When $x = 200$, the total cost is:

$$C = 13.50(200) + 48,950 = 51,250$$

So the average cost per unit is:

$$\text{Average cost per unit} = \frac{51,250}{200} = 256.25$$

Rounded to the nearest cent, the answer is $\$ 258.25$, so the correct choice is D.

The Cost Function for a Certain Model of a Digital C=13.50x+48,950C = 13.50 x + 48,950C=13.50x+48,950

The Cost Function for a Certain Model of a Digital $C = 13.50 x + 48,950$