Questions: Homework 1 Part 2 of 4 Points: 0 of 1 A charter fight charges a fare of 300 per person plus 45 per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats. a. Find an expression for the total revenue received for the flight R(x). R(x) = 30000 + 4200x - 45x^2 b. Choose the correct graph of the function, R(x), below.

Homework 1
Part 2 of 4
Points: 0 of 1

A charter fight charges a fare of 300 per person plus 45 per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats.
a. Find an expression for the total revenue received for the flight R(x).
R(x) = 30000 + 4200x - 45x^2
b. Choose the correct graph of the function, R(x), below.

Transcript text: Homework 1 Part 2 of 4 Points: 0 of 1 A charter fight charges a fare of $\$ 300$ per person plus $\$ 45$ per person for each unsold seat on the plane. The plane holds 100 passengers. Let x represent the number of unsold seats. a. Find an expression for the total revenue received for the flight $R(x)$. \[ R(x)=30000+4200 x-45 x^{2} \] b. Choose the correct graph of the function, $\mathrm{R}(\mathrm{x})$, below.

Solution

Solution Steps

Step 1: Analyze the problem and define variables

Let $x$ represent the number of unsold seats. The plane holds 100 passengers. The fare is $300 per person plus $45 per person for each unsold seat. We want to find the total revenue, R(x).

Step 2: Formulate an expression for the total revenue

The number of sold seats is $100 - x$. The fare per person is $300 + 45x$. The total revenue is the product of the number of sold seats and the fare per person: $R(x) = (100 - x)(300 + 45x)$ $R(x) = 30000 + 4500x - 300x - 45x^2$ $R(x) = 30000 + 4200x - 45x^2$

Step 3: Determine the appropriate graph

The function $R(x)$ is a quadratic function with a negative leading coefficient (-45), meaning it opens downwards and represents a parabola. The graph of this function should be a parabola with its vertex representing the maximum revenue. We are given that x represents the number of unsold seats and therefore $0 \le x \le 100$, so the correct graph should intersect the x-axis at x=0 and x=100 (approximately). Also, $R(0) = 30000$.