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: \(R(x) = -35x^2 + 3200x + 30000\).