Answer
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Step 1:: Identify the given function and its intercepts
The x-axis intercepts can be found by setting $f(x) = 0$ and solving for $x$.
Step 2:: Solve for the x-axis intercepts
So, the graph intersects the x-axis at $x = 0$ and $
\begin{align*} f(x) &= 0 \ - 500x^2 + 25000x &= 0 \ \end{align*} x = 50$.
Step 3:: Understand the meaning of the x-axis intercepts
The x-axis intercepts represent the unit prices at which the company receives no revenue. This is because the number of items sold at these prices would be zero (assuming the company doesn't give away the product for free).
Step 4:: Answer the question
Therefore, the correct answer is option C: The unit price, in dollars, of the product that will result in a revenue of $\$ 0$.
Final Answer
Therefore, the correct answer is option C: The unit price, in dollars, of the product that will result in a revenue of $\$ 1$.
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