Questions: The average cost per set for the production of television sets is given by C̅(x) = (980 + 60x + 0.2x^2) / x where x is the number of hundreds of units produced. Complete parts (a) through (d) below. b. Graph this function using the window [0,50] by [0,300].

Solution Steps

The given function represents the average cost per set for producing television sets:
$\bar{C}(x) = \frac{980 + 60x + 0.2x^2}{x}$ where x is the number of hundreds of units produced. The general shape of a graph is determined by examining its behavior at key points and as x approaches infinity.

Part (a) requires choosing the correct graph of the function without a specified window. We should look for a graph that starts with a high value when x is close to 0 (since the 980/x term will dominate) and decreases but eventually increases again as the x² term starts to dominate at larger values of x. This rules out the graphs showing a linear function or a strictly decreasing function.

The correct graph for part (a) is A.

Part (b) specifies a window of [0, 50] by [0, 300] for x and $\bar{C}(x)$, respectively. We need to find a graph matching the general shape from Step 2 within this window. When x is close to zero, $\bar{C}(x)$ will be large. Then, $\bar{C}(x)$ decreases and eventually increases again.

The correct graph for part (b) is B.

Final Answer: