Final answer:
To find the price for each seat at maximum revenue, we need to find the number of unsold seats and calculate the total revenue. By finding the vertex of the quadratic equation, we can determine the number of unsold seats and the price per seat. The price for each seat at maximum revenue is approximately $225.
Step-by-step explanation:
To determine the price for each seat that is received when revenue is at its maximum, we need to find the number of unsold seats and calculate the total revenue. Let's assume that x represents the number of unsold seats. The total revenue is given by the formula: 300(200-x) + 2x. To find the maximum revenue, we can find the vertex of the quadratic equation. The x-coordinate of the vertex gives us the number of unsold seats, and we can plug it back into the equation to find the price per seat.
First, let's rewrite the equation as: -2x^2 + 596x + 60000. The x-coordinate of the vertex is given by the formula: -b/2a. Substituting the values, we get x = 596/(2*(-2)) = 596/(-4) = -149.
Since we can't have a negative number of unsold seats, we take the absolute value: |x| = |(-149)| = 149. Plug it back into the equation: 300(200-149) + 2(149) = 45100.
The price for each seat at maximum revenue is $45100/200 ≈ $225. Hence, the correct option is (B) Between 275 and 325.