A charter flight charges a fare of $\$ 300$ per person plus $\$ 35$ per person for each unsold seat on the plane. The plane holds 100 passengers. Let $x$ represent the number of unsold seats. Complete parts (a) through (d).
(a) Find an expression for the total revenue received for the flight $R(x)$. (Hint: Multiply the number of people flying, $100-x$, by the price per ticket.)
\[
R(x)=\square
\]

Step 1 ：Let's denote the number of unsold seats as \(x\). The total number of passengers the plane can hold is 100, so the number of passengers that are flying is \(100 - x\).

Step 2 ：The fare for each passenger is \(\$300\) plus an additional \(\$35\) for each unsold seat. So, the total fare for each passenger is \(\$300 + \$35x\).

Step 3 ：The total revenue \(R(x)\) received for the flight is the number of passengers times the fare for each passenger. So, \(R(x) = (100 - x) \cdot (300 + 35x)\).

Step 4 ：Now, let's simplify this expression using Python.

Step 5 ：After simplifying, we get \(R(x) = 30000 - 300x + 3500x - 35x^2\).

Step 6 ：Finally, we can rearrange the terms to get the final answer: \(R(x) = -35x^2 + 3200x + 30000\).