Question

in example 2 we saw that airbus a330-300s seat 330 passengers and cost $260 million each, boeing 767-300ers seat 270 passengers and cost $220 million each, while boeing dreamliner 787-9s seat 240 passengers and cost $290 million each. you are the purchasing manager of an airline company and have a spending goal of $3,780 million for the purchase of new aircraft to seat a total of 4,230 passengers. your company has a policy of supporting u.s. industries, and you have been instructed to buy twice as many boeings as airbuses. given the selection of three aircraft, how many of each should you order?

Answer 1

To determine the number of each type of aircraft to purchase, the purchasing manager must solve a system of equations that reflects the seating capacity, cost, and policy constraint that requires buying twice as many Boeings as Airbuses.

Step-by-step explanation:

The student is looking to apply mathematical skills to solve a practical problem involving the purchase of commercial aircraft under certain budgetary and policy constraints. Specifically, the task is to determine how many Airbus A330-300s, Boeing 767-300ERs, and Boeing Dreamliners 787-9s to order such that the airline can seat a total of 4,230 passengers, with a spending limit of $3,780 million, and adhering to the policy of purchasing twice as many Boeings as Airbuses.

To find the solution, one must set up a system of equations that takes into account the number of planes, the cost of each plane, the seating capacity, and the policy requirement. The variables can be defined as: x for Airbus A330-300s, y for Boeing 767-300ERs, and z for Boeing Dreamliner 787-9s. The system of equations would look like this:

• Number of seats equation: 330x + 270y + 240z = 4,230
• Cost equation: 260x + 220y + 290z ≤ 3,780 (in millions)
• Policy constraint: y + z = 2x

By solving this system of equations, the airline can figure out exactly how many of each type of aircraft to purchase to meet all criteria.