A domestic airline has designed a new line of passenger aircraft. The company wants to fit the maximum number of people comfortably in each aircraft to maximize its revenue. It will install custom seating and choose the size of the pitch of each seat for the new aircraft models. The pitch of a seat is the distance between a point on the back of a seat and the same point located on the seat in front of it. (See the diagram below.) Seat pitch is an indicator of the leg room and reclining space available to each customer.

Part A
The new aircraft model has a passenger section that is 100 feet long. Using appropriate variables, write an equation expressing the relationship between the number of rows of seats on the airplane and the seat pitch. Assume that the seat backs in the last row are flush against the wall.

Part B
The airline would like to use your equation from part a to develop a function. The function will determine the number of rows that can fit in the aircraft based on a chosen pitch size. Rearrange the equation from part a to create a function where the pitch size is the input and the number of rows is the output.

Part C
As part of the design process, the company wants to try different combinations of number of rows and seat pitches. Use the equation from part a or the function from part b to complete the table below.

Part D
Describe the relationship between the number of rows on the aircraft and the size of the seat pitch. What type of variation does it show?

Part E
The company wants a visual representation to better understand the relationship between the number of rows and the seat pitch. You will use a coordinate graph to show this representation. Graph the function you derived in part b using the Edmentum Graphing Tool. Paste your graph below.

Part F
The company's research shows that passengers find it uncomfortable if the seat pitch is less than 2.5 feet. Write an equation that illustrates that the pitch size must be exactly 2.5 feet.

Part G
Graph the equations from parts e and f on the same plane using the Edmentum Graphing Tool. Paste your graph below.

Part H
Assume there are five passenger seats per row. How many seats would be lost if the plane improved leg room by adding 0.5 foot to the pitch of the seats, increasing the pitch size to 3 feet?

Part I
Assume that an average passenger pays $400 for a single trip on this aircraft. If the aircraft reaches its full seating capacity for the trip, what will be the difference in the airline's revenue if it chooses to use a pitch size of 3 feet instead of 2.5 feet?