Let $C(x) = \left( \frac{x}{10}-1 \right)^3+1$ be a firm's total cost, in millions of dollars, for producing a quantity $x$ thousand units of an item.

(a) On a separate piece of paper, sketch a graph of $C(x)$.

(b) Let $R(x)$ be the revenue to the firm (in millions of dollars) for selling a quantity $x$ thousand units of the good. Suppose $R(x)= \frac{x}{10}$. What does this tell you about the price of each unit?
A. The more units they sell, they charge less per single unit sold.
B. The price they charge for a single unit does not depend on the number of units they sell.
C. The more units they sell, they charge more per single unit sold.

(c) Profit equals revenue minus cost. For what value(s) of $x$ does the firm:
(Recall that $x$ is measured in thousands of units. So for example $x = 5$ should be entered as $5000$, not as $5$ or as $5,000$. Only enter commas in each of your answers below to separate values or endpoints of your intervals.)
break even? units (If there is more than one answer, enter your values in a comma separated list.)
make a profit? units help (inequalities)
lose money? units help (inequalities)